1. 2018 Geometry Bootcamp
2018
Circles, Geometric Measurement, and Geometric Properties with Equations
2018 Geometry Bootcamp

2. MAFS.912.G-C.1.1
Eric explains that all circles are similar using the argument shown.
Let there be two circles, circle A and circle B.
There exists a translation that can be performed on circle A such that it will have the same center as circle B.
Thus, there exists a sequence of transformations that can be performed on circle A to obtain circle B.
Therefore, circle A is similar to circle B.
Since circle A and circle B can be any circles, all circles are similar.
Which statement could be step 3 of the argument?
There exists a reflection that can be performed on circle A such that it will have the same radius as circle B.
There exists a dilation that can be performed on circle A such that it will have the same radius as circle B.
There exists a reflection that can be performed on circle B such that it will have the same radius as circle A.
There exists a dilation that can be performed on circle B such that it will have the same radius as circle A.
Groups 1, 2, and 3 B

3. 2018 Geometry Bootcamp
MAFS.912.G-C.1.1
Which describes how Circle C can be transformed to show that Circle D is a similar figure?
translation of Circle 𝐶: (𝑥, 𝑦)→(𝑥+3, 𝑦+8); dilation of the image with center (4, –1) and scale factor 6
translation of Circle 𝐶: (𝑥, 𝑦)→(𝑥+8, 𝑦+3); dilation of the image with center (4, –1) and scale factor 1 6
translation of Circle 𝐶: (𝑥, 𝑦)→(𝑥+3, 𝑦+8); dilation of the image with center (4, –1) and scale factor 1 6
translation of Circle 𝐶: (𝑥, 𝑦)→(𝑥+8, 𝑦+3); dilation of the image with center (4, –1) and scale factor 6
Groups 1, 2, and 3 B
2018 Geometry Bootcamp

4. 2018 Geometry Bootcamp
MAFS.912.G-C.1.1
Circle 𝐽 is located in the first quadrant with center 𝑎, 𝑏 and radius 𝑠. Felipe transforms circle 𝐽 to prove that it is similar to any circle centered at the origin with radius 𝑡.
Which sequence of transformations did Felipe use?
Translate Circle J by 𝑥, 𝑦 → 𝑥+𝑎, 𝑦+𝑏 and dilate by a factor of 𝑡 𝑠 .
Translate Circle J by 𝑥, 𝑦 → 𝑥+𝑎, 𝑦+𝑏 and dilate by a factor of 𝑠 𝑡 .
Translate Circle J by 𝑥, 𝑦 → 𝑥−𝑎, 𝑦−𝑏 and dilate by a factor of 𝑡 𝑠 .
Translate Circle J by 𝑥, 𝑦 → 𝑥−𝑎, 𝑦−𝑏 and dilate by a factor of 𝑠 𝑡 .
Groups 2 and 3 C
2018 Geometry Bootcamp

5. MAFS.912.G-C.1.2 In the diagram below, 𝑚 𝐴𝐵𝐶 =268°.
2018 Geometry Bootcamp
MAFS.912.G-C.1.2
In the diagram below, 𝑚 𝐴𝐵𝐶 =268°.
What is the number of degrees in the measure of ∠𝐴𝐵𝐶?
134°
92°
68°
46°
Groups 1, 2, and 3 D
2018 Geometry Bootcamp

6. MAFS.912.G-C.1.2 The diagram shows circle 𝐶.
2018 Geometry Bootcamp
MAFS.912.G-C.1.2
The diagram shows circle 𝐶.
Which of these statements is true?
m∠𝑃𝐾𝑄= 1 2 m∠𝑃𝑁𝑄
m∠𝑃𝐾𝑄= 1 2 m∠𝑃𝐶𝑄
m∠𝑃𝐾𝑄=m∠𝑃𝐶𝑄
m∠𝑃𝐾𝑄=2m∠𝑃𝐶𝑄
Groups 1, 2, and 3 B
2018 Geometry Bootcamp

7. 2018 Geometry Bootcamp
MAFS.912.G-C.1.2
𝐶𝐾 is the diameter of Circle 𝑂. If 𝑚 𝐽𝐶 =19𝑥° and 𝑚 𝐽𝐾 =[9 𝑥+2 −6]°, find the value of 𝑥.
4 5
5 6 4 6
Groups 1, 2, and 3 D
2018 Geometry Bootcamp

8. 2018 Geometry Bootcamp
MAFS.912.G-C.1.2
Maggie and Wei are measuring the distance across a circular fountain indirectly as shown in the diagram.
They find that the length of 𝑅𝑆 is 15 meters and the length of 𝑆𝑇 is 9 meters. 𝑅𝑆 is tangent to circle 𝐹 and point 𝑇 is on 𝐹𝑆 . To the nearest meter, what is the
diameter of the fountain?
Enter your answer in the box.
Groups 1, 2, and 3 16
2018 Geometry Bootcamp

9. MAFS.912.G-C.1.2 Points A, B, and D lie on circle C.
2018 Geometry Bootcamp
MAFS.912.G-C.1.2
Points A, B, and D lie on circle C.
Determine the measure of the indicated angles given that 𝑚∠𝐴= 30°.
Enter the measures in the boxes.
𝑚∠𝐵𝐶𝐷=
60°
Groups 1, 2, and 3
𝑚∠𝐴𝐵𝐷=
90°
2018 Geometry Bootcamp

10. 2018 Geometry Bootcamp
MAFS.912.G-C.1.2
The figure below shows concentric circles, both centered at O.
Chord XY is tangent to the smaller circle.
The radius of the larger circle is 15 cm.
The radius of the smaller circle is 12 cm.
What is the length of chord XY?
27 cm
24 cm
18 cm
10 cm
Groups 1, 2, and 3 C
2018 Geometry Bootcamp

11. MAFS.912.G-C.1.3 Quadrilateral 𝐸𝐹𝐺𝐻 is inscribed in a circle as shown.
2018 Geometry Bootcamp
MAFS.912.G-C.1.3
Quadrilateral 𝐸𝐹𝐺𝐻 is inscribed in a circle as shown.
m∠𝐹= 4𝑥+10 °, m∠𝐺= 2𝑥−5 °, and m∠𝐻= 3𝑥−5 °. What is the value of 𝑥? 20 25 38 40
Groups 1, 2, and 3 B
2018 Geometry Bootcamp

12. MAFS.912.G-C.1.3 Quadrilateral FGHJ and circle O are shown.
2018 Geometry Bootcamp
MAFS.912.G-C.1.3
Quadrilateral FGHJ and circle O are shown.
Given: m∠𝐽𝐹𝐺=56°
Which statement, if true, would help prove that quadrilateral FGHJ is inscribed in Circle O and why?
m∠𝐺𝐻𝐽=56°; for a quadrilateral inscribed in a circle, opposite angles are congruent.
m∠𝐹𝐺𝐻=124°; for a quadrilateral inscribed in a circle, adjacent angles are supplementary.
m∠𝐺𝐻𝐽=124°; for a quadrilateral inscribed in a circle, opposite angles are supplementary.
m∠𝐹𝐺𝐻=56°; for a quadrilateral inscribed in a circle, adjacent angles are congruent.
Groups 1, 2, and 3 C
2018 Geometry Bootcamp

13. 2018 Geometry Bootcamp
MAFS.912.G-C.1.3
In the circle shown, the measure of ∠𝐶 is 110°, and the measure of ∠𝐷 is 80°.
Match the correct angle measure to each box for ∠A and ∠B.
70°
80°
110°
140°
220°
100°
Measure of ∠A
Measure of ∠B
70°
Groups 1, 2, and 3
100°
2018 Geometry Bootcamp

14. 2018 Geometry Bootcamp
MAFS.912.G-C.1.3
Select all statements that are valid when a triangle is inscribed in a circle.
the circle is circumscribed about the triangle.
the perpendicular bisectors of the triangle may be constructed to find the center of the circle.
the center of the circumscribed circle must always be in the interior of the triangle.
the vertices of the triangle are equidistant from the center of the circle.
the triangle must be isosceles.
Groups 2 and 3
2018 Geometry Bootcamp

15. MAFS.912.G-C.2.5 Points A, B, D, and E lie on circle C.
2018 Geometry Bootcamp
MAFS.912.G-C.2.5
Points A, B, D, and E lie on circle C.
What is the length of arc ADB?
8π 3 in.
4π in.
16 3 π in.
8π in.
Groups 1, 2, and 3 A
2018 Geometry Bootcamp

16. 2018 Geometry Bootcamp
MAFS.912.G-C.2.5
A sector is part of a circle’s area that is defined by a central angle. The ratio of the sector’s area, 𝐴, to the circle’s area, 𝜋 𝑟 2 , is identical to the ratio of the central angle, 𝜃, to the total measure of the circle, 360°.
Which option represents the formula for the area of a sector?
𝐴= 360° 𝜃 𝜋 𝑟 2
𝐴=𝜃𝜋 𝑟 2
𝐴=360°𝜋 𝑟 2
𝐴= 𝜃 360° 𝜋 𝑟 2
Groups 1, 2, and 3 D
2018 Geometry Bootcamp

17. 2018 Geometry Bootcamp
MAFS.912.G-C.2.5
A spotlight has a beam that travels 100 feet and covers an area intercepted by an 84° angle, as shown.
To the nearest square foot, what area does the spotlight cover?
Enter your answer in the box.
7, 330
Groups 1, 2, and 3
2018 Geometry Bootcamp

18. Subtended Central Angle
2018 Geometry Bootcamp
MAFS.912.G-C.2.5
The circle with center 𝐹 is divided into sectors. In circle 𝐹, 𝐸𝐵 is a diameter. The length of 𝐹𝐵 is 3 units
Drag and drop each arc length to its subtended central angle.
Subtended Central Angle
Arc Length in radians
∠𝐴𝐹𝐵
∠𝐵𝐹𝐶
∠𝐶𝐹𝐷
∠𝐴𝐹𝐸 2𝜋
3𝜋 4
Groups 2 and 3
𝜋 2
𝜋 2 𝜋 2𝜋
3𝜋 4
𝜋 4 𝜋
2018 Geometry Bootcamp

19. 2018 Geometry Bootcamp
MAFS.912.G-GMD.1.1
To find the formula for the area of a circle, the circle can be cut into “slices,” as indicated below. Which statement best describes the process being used?
To find the area of a circle, rearrange the pieces to form a “parallelogram” with a base of 𝜋𝑟 and a height of 𝑟.
To find the area of a circle, rearrange the pieces to form a “parallelogram” with a base of 2𝜋𝑟 and a height of 𝑟.
To find the area of a circle, rearrange the pieces to form a “parallelogram” with a base of 𝜋𝑟 and a height of 𝑟.
To find the area of a circle, rearrange the pieces to form a “parallelogram” with a base of 1 2 𝜋𝑟 and a height of 2𝑟.
Groups 1, 2, and 3 C
2018 Geometry Bootcamp

20. 2018 Geometry Bootcamp
MAFS.912.G-GMD.1.1
The cylinder and the cone shown below have the same height, and their bases have the same radius.
How does the volume of the cylinder 𝑉 𝑐𝑦𝑙 compare to the volume of the cone 𝑉 𝑐𝑜𝑛𝑒 ?
𝑉 𝑐𝑦𝑙 =2 𝑉 𝑐𝑜𝑛𝑒
𝑉 𝑐𝑦𝑙 = 1 3 𝑉 𝑐𝑜𝑛𝑒
𝑉 𝑐𝑦𝑙 − 𝑉 𝑐𝑜𝑛𝑒 =3 𝑉 𝑐𝑜𝑛𝑒
𝑉 𝑐𝑦𝑙 − 𝑉 𝑐𝑜𝑛𝑒 =2 𝑉 𝑐𝑜𝑛𝑒
Groups 1, 2, and 3 D
2018 Geometry Bootcamp

21. 2018 Geometry Bootcamp
MAFS.912.G-GMD.1.1
A circle with radius 𝑟 is divided into sectors as shown. The sectors are arranged in a shape that resembles a parallelogram.
Which of the given statements are true? Select all that apply.
The length of base 𝑃𝑆 of the parallelogram 𝑃𝑄𝑅𝑆 is approximately equal to 1 2 𝜋𝑟.
The length of base 𝑃𝑆 of the parallelogram 𝑃𝑄𝑅𝑆 is approximately equal to 𝜋𝑟.
The length of base 𝑃𝑆 of the parallelogram 𝑃𝑄𝑅𝑆 is approximately equal to 2𝜋𝑟.
The height of the parallelogram 𝑃𝑄𝑅𝑆 is approximately equal to 𝜋.
The height of the parallelogram 𝑃𝑄𝑅𝑆 is approximately equal to 𝑟.
The area of the parallelogram 𝑃𝑄𝑅𝑆 is approximately equal to 2𝜋𝑟.
The area of the parallelogram 𝑃𝑄𝑅𝑆 is approximately equal to 2𝜋 𝑟 2 .
The area of the parallelogram 𝑃𝑄𝑅𝑆 is approximately equal to 𝜋 𝑟 2 .
Groups 1, 2, and 3
2018 Geometry Bootcamp

22. 2018 Geometry Bootcamp
MAFS.912.G-GMD.1.3
An ice cream waffle cone can be modeled by a right circular cone with a base diameter of 6.6 centimeters and a volume of 54.45𝜋; cubic centimeters. What is the number of centimeters in the height of the waffle cone?
3 3 4 5 15
24 3 4
Groups 1, 2, and 3 C
2018 Geometry Bootcamp

23. 2018 Geometry Bootcamp
MAFS.912.G-GMD.1.3
To completely cover a spherical ball, a ball company uses a total area of
36 square inches of material. What is the maximum volume the ball can have?
27𝜋 cubic inches
36 𝜋 cubic inches
36 𝜋 cubic inches
27 𝜋 cubic inches
Groups 1, 2, and 3 C
2018 Geometry Bootcamp

24. 2018 Geometry Bootcamp
MAFS.912.G-GMD.1.3
A regular pyramid has a square base. The perimeter of the base is 36 inches and the height of the pyramid is 15 inches. What is the volume of the pyramid in cubic inches?
180
405
540
1215
Groups 1, 2, and 3 B
2018 Geometry Bootcamp

25. 2018 Geometry Bootcamp
MAFS.912.G-GMD.1.3
A soft drink company wants to increase the volume of the cylindrical can they sell soft drinks in by 25%. The company wants to keep the 5-inch height of the can the same. The radius of the can is currently 2.5 inches. Approximately how much should the radius of the can be increased?
0.245 inches
0.250 inches
0.278 inches
0.295 inches
Groups 1, 2, and 3 D
2018 Geometry Bootcamp

26. 2018 Geometry Bootcamp
MAFS.912.G-GMD.1.3
Trevon is shopping for an art project for his class of third graders. He wants each of his 30 students to have a ball of modeling clay 10 centimeters in diameter. The modeling clay is sold in cylindrical rolls that are 15 centimeters long and 4 centimeters in diameter. How many rolls of clay does he need to buy?
Enter your answer in the box. 84
Groups 1, 2, and 3
2018 Geometry Bootcamp

27. 2018 Geometry Bootcamp
MAFS.912.G-GMD.1.3
The table shows the approximate measurements of the Great Pyramid of Giza in Egypt and the Pyramid of Kukulcan in Mexico.
Pyramid
Height
(meters)
Area of Base
(square meters)
Great Pyramid of Giza
147
52,900
Pyramid of Kukulcan 30
3,025
Approximately what is the difference between the volume of the Great Pyramid of Giza and the volume of the Pyramid of Kukulcan?
Groups 1, 2, and 3
1,945,000 cubic meters
2,562,000 cubic meters
5,835,000 cubic meters
7,686,000 cubic meters B
2018 Geometry Bootcamp

28. 2018 Geometry Bootcamp
MAFS.912.G-GMD.1.3
Anders is using coats to make plaster figures. He has a cylinder cast that has a diameter of 8 inches and is 24 inches tall. Anders uses a cone- shaped container with a diameter of 12 inches and a height of 16 inches to fill his casts. How many cone-shaped containers full of plaster will he need to completely fill the cylinder cast?
Enter your answer in the box. 2
Groups 1, 2, and 3
2018 Geometry Bootcamp

29. 2018 Geometry Bootcamp
MAFS.912.G-GMD.1.3
A popcorn container is made from a cone with a portion of the cone removed and sealed, as shown. The removed portion of the cone has a height of 1 3 𝑚.
Create an expression, using 𝑚, that represents the volume, in cubic centimeters, of the popcorn container.
1 3 𝑚 𝑚 𝜋− 𝑚 𝜋 𝑚 3
Groups 2 and 3
2018 Geometry Bootcamp

30. 2018 Geometry Bootcamp
MAFS.912.G-GMD.2.4
The figure shows a plane slicing through a cone. The plane is neither parallel nor perpendicular to the base of the cone, and the plane does not intersect the base of the cone. What is the shape of the cross section created by the slice?
Circle
Ellipse
Parabola
Triangle
Groups 1, 2, and 3 B
2018 Geometry Bootcamp

31. 2018 Geometry Bootcamp
MAFS.912.G-GMD.2.4
On the coordinate plane, △ART is shown with points 𝑅 and 𝑇 plotted on the 𝑦-axis.
What three-dimensional figure is created by rotating △ART around the 𝑦-axis?
Cone
Sphere
Cylinder
Pyramid
Groups 1, 2, and 3 A
2018 Geometry Bootcamp

32. 2018 Geometry Bootcamp
MAFS.912.G-GMD.2.4
Which solid of revolution is produced by rotating the shape below 360° about the given axis? A B C D
Groups 1, 2, and 3 B
2018 Geometry Bootcamp

33. MAFS.912.G-GMD.2.4
Which of the following two-dimensional cross sections are circles?
Select all that apply.
any cross section of a sphere
horizontal cross section of a cube
cross section of a cone parallel to its base
cross section of a cone perpendicular to its base
cross section of a right cylinder parallel to its base
cross section of a pyramid perpendicular to its base
Groups 1, 2, and 3

34. MAFS.912.G-GMD.2.4
What are the possible cross sections of a right circular cone?
Select all that apply.
Ellipse
Triangle
Circle
Parabola
Rectangle
Groups 2 and 3

35. 2018 Geometry Bootcamp
MAFS.912.G-GMD.2.4
A triangle has vertices at (0, 0), (0, 9), and (4, 0).
If the triangle is revolved about the 𝑥-axis, what 3-dimensional solid is formed?
a pyramid with a square base of 4 units by 4 units and a height of 9 units
a pyramid with a square base of 9 units by 9 units and a height of 4 units
a cone with a diameter of 8 units and a height of 9 units
a cone with a diameter of 18 units and a height of 4 units
Groups 2 and 3 D
2018 Geometry Bootcamp

36. MAFS.912.G-GPE.1.1
A circle has its center at (−2, 3) and point (4, 6) is on its circumference. What is the correct written equation of the circle?
𝑥 𝑦−2 2 =85
𝑥− 𝑦+2 2 =45
𝑥− 𝑦+3 2 =85
𝑥 𝑦−3 2 =45
Groups 1, 2, and 3 D

37. 2018 Geometry Bootcamp
MAFS.912.G-GPE.1.1
Write the equation of a circle with a radius of 5 units and a center at (-3, 4)?
𝑥 𝑦−4 2 =25
Groups 1, 2, and 3
2018 Geometry Bootcamp

38. 2018 Geometry Bootcamp
MAFS.912.G-GPE.1.1
In the 𝑥𝑦−coordinate plane shown, points B, E, G, and I are on the circle with center H.
Part A
What is the equation of the circle with center H?
𝑥− 𝑦−2 2 = 10
𝑥− 𝑦−2 2 =10
𝑥 𝑦+2 2 = 10
𝑥 𝑦+2 2 =10
Groups 1, 2, and 3 B
2018 Geometry Bootcamp

39. 2018 Geometry Bootcamp
MAFS.912.G-GPE.1.1
In the 𝑥𝑦−coordinate plane shown, points B, E, G, and I are on the circle with center H.
Part B
The equation 𝑥 2 + 𝑦 2 −6𝑥+2𝑦+5=0 represents the circle with which center? B E G I
Groups 1, 2, and 3 D
2018 Geometry Bootcamp

40. 2018 Geometry Bootcamp
MAFS.912.G-GPE.1.1
What is the radius of the circle with equation 𝑥 2 + 𝑦 2 +6𝑥=54+2𝑦? 8
Groups 1, 2, and 3
2018 Geometry Bootcamp

41. 2018 Geometry Bootcamp
MAFS.912.G-GPE.1.1
The equation 𝑥 2 + 𝑦 2 − 4𝑥 + 2𝑦 = 𝑏 describes a circle.
Part A
Determine the y-coordinate of the center of the circle.
Enter your answer in the box. -1
Part B
The radius of the circle is 7 units. What is the value of b in the equation?
Enter your answer in the box.
Groups 2 and 3 44
2018 Geometry Bootcamp

42. 2018 Geometry Bootcamp
MAFS.912.G-GPE.2.4
Select the responses that correctly complete the sentence.
Given △ABC with A(5, 4), B(2, −2), and C(7, −1).
△ABC is classified as because
Groups 1, 2, and 3
2018 Geometry Bootcamp

43. 2018 Geometry Bootcamp
MAFS.912.G-GPE.2.4
△RST has vertices at R(7, –4), S(12, –12), and T(2, –12). What type of triangle is △RST?
Equilateral
Isosceles
Scalene
Right
Groups 1, 2, and 3 B
2018 Geometry Bootcamp

44. 2018 Geometry Bootcamp
MAFS.912.G-GPE.2.4
The vertices of quadrilateral EFGH are E(−7, 3), F(−4, 6), G(5, −3), and H(2, −6). What kind of quadrilateral is EFGH?
A trapezoid
B square
C rectangle that is not a square
D rhombus that is not a square
Groups 1, 2, and 3 C
2018 Geometry Bootcamp

45. 2018 Geometry Bootcamp
MAFS.912.G-GPE.2.4
Quadrilateral 𝑅𝑆𝑇𝑈 has vertices R(1, 3), S(4, 1), T(1, -3) and U(-2, −1).
Which statement about quadrilateral 𝑅𝑆𝑇𝑈 is true?
Since the diagonals of quadrilateral 𝑅𝑆𝑇𝑈 are not congruent, it is not a rectangle.
Since the adjacent sides of quadrilateral 𝑅𝑆𝑇𝑈 have equal slopes, it is not a rectangle.
Since the diagonals of quadrilateral 𝑅𝑆𝑇𝑈 are congruent, it is a rectangle.
Since the adjacent sides of quadrilateral 𝑅𝑆𝑇𝑈 have equal slopes that are negative reciprocals, it is a rectangle.
Groups 2 and 3 A
2018 Geometry Bootcamp

46. 2018 Geometry Bootcamp
MAFS.912.G-GPE.2.5
Consider the line given by the equation 5𝑥+2𝑦=8. Which of the following gives the equation of a line parallel to the given line but with a different 𝑦−intercept?
y= −5𝑥 2 +4
y= −5𝑥 2 +8
y= −2𝑥 5 +4
y= −2𝑥 5 +8
Groups 1, 2, and 3 B
2018 Geometry Bootcamp

47. 2018 Geometry Bootcamp
MAFS.912.G-GPE.2.5
Given the line 3𝑥−9𝑦=18, what is the equation of a line that is perpendicular to the given line at the given line’s 𝑥−intercept?
𝑦= 1 3 𝑥−2
𝑦= 1 3 𝑥+6
𝑦=−3𝑥+6
𝑦=−3𝑥+18
Groups 1, 2, and 3 D
2018 Geometry Bootcamp

48. 2018 Geometry Bootcamp
MAFS.912.G-GPE.2.5
What is the equation of the line through (3, 7) that is perpendicular to the line through points (-1, -2) and (5, 3)?
𝒚=− 𝟔 𝟓 𝒙+ 𝟓𝟑 𝟓
Groups 1, 2, and 3
2018 Geometry Bootcamp

49. 2018 Geometry Bootcamp
MAFS.912.G-GPE.2.5
Create the equation of a line that is perpendicular to 2𝑦= 𝑥 and passes through the point −2, 8 .
𝒚=−𝟑𝒙+𝟐
Groups 1, 2, and 3
2018 Geometry Bootcamp

50. 2018 Geometry Bootcamp
MAFS.912.G-GPE.2.5
A line segment has endpoints 𝐽(2, 4) and 𝐿(6, 8). The point 𝐾 is the midpoint of 𝐽𝐿. What is an equation of a line perpendicular to 𝐽𝐿 and passing through 𝐾?
𝑦 = −𝑥 + 10
𝑦 = −𝑥 – 10
𝑦 = 𝑥 + 2
𝑦 = 𝑥 – 2
Groups 2 and 3 A
2018 Geometry Bootcamp

51. 2018 Geometry Bootcamp
MAFS.912.G-GPE.2.6
On a coordinate plane, the endpoints of line segment 𝐽𝐾 are 𝐽(−10, 12) and 𝐾(8, −12). Point 𝐿 lies on segment 𝐽𝐾 and divides it into two segments such that the ratio of 𝐽𝐿 to 𝐿𝐾 is 5:1.
What are the coordinates of point 𝐿?
−7, 8
−6.4, 7.2
4.4, −7.2
5, −8
Groups 1, 2, and 3 D
2018 Geometry Bootcamp

52. 2018 Geometry Bootcamp
MAFS.912.G-GPE.2.6
In the 𝑥𝑦−coordinate plane, the coordinates of point 𝑆 are (−2, −6), and the coordinates of point 𝑇 are (18, 9). Point 𝑄 lies on line segment 𝑆𝑇 so that the ratio of the distance from point 𝑆 to point 𝑄 to the distance from point 𝑄 to point 𝑇 is 2 to 3. What are the coordinates of point 𝑄?
Enter your answer in the boxes.
The coordinates of point 𝑄 are , 6
Groups 1, 2, and 3
2018 Geometry Bootcamp

53. MAFS.912.G-GPE.2.6
A line segment has endpoints 𝑆(−9, −4) and 𝑇(6, 5). Point 𝑅 lies on 𝑆𝑇 such as the ratio of 𝑆𝑅 to 𝑅𝑇 is 2:1.
What are the coordinates of point 𝑅?
Enter your answer in the boxes.
The coordinates of point 𝑅 are , 1 2
Groups 1, 2, and 3

54. 2018 Geometry Bootcamp
MAFS.912.G-GPE.2.6
Point 𝑃 is between 𝐷(2, 5) and 𝐹(5, −1). What are the coordinates of 𝑃 along the directed 𝐷𝐹 if the ratio of 𝐷𝑃 to 𝑃𝐹 is 1:2?
Enter the correct coordinates in the boxes.
Value of the 𝑥−coordinate:
Value of the 𝑦−coordinate: 3
Groups 1, 2, and 3
2018 Geometry Bootcamp

55. 2018 Geometry Bootcamp
MAFS.912.G-GPE.2.6
Line segment 𝐽𝐾 in the 𝑥𝑦-coordinate plane has endpoints with coordinates (−4, 11) and (8, −1). What are two possible locations for point 𝑀 so that 𝑀 divides 𝐽𝐾 into two parts with lengths in a ratio of 1:3? Indicate both locations.
−2, 9
−1, 8
0, 7
1, 6
3, 4
4, 3
5, 2
(6, 1)
Groups 2 and 3
B, G
2018 Geometry Bootcamp

56. 2018 Geometry Bootcamp
MAFS.912.G-GPE.2.7
On the set of axes below, the vertices of ∆𝑃𝑄𝑅 have coordinates 𝑃 −6, 7 , 𝑄 2, 1 and 𝑅(−1, −3).
What is the area of ∆𝑃𝑄𝑅 ? 10 20 25 50
Groups 1, 2, and 3 C
2018 Geometry Bootcamp

57. 2018 Geometry Bootcamp
MAFS.912.G-GPE.2.7
Find the perimeter of the figure. Round to the nearest hundredth.
23.61
Groups 1, 2, and 3
2018 Geometry Bootcamp

58. 2018 Geometry Bootcamp
MAFS.912.G-GPE.2.7
In △𝐴𝐵𝐶, ∠𝐵 is a right angle. The coordinates for each point are 𝐴(10, 7), 𝐵(5, 9), and 𝐶(3, 4).
Rounded to the nearest tenth, what is the area, in square units, of △𝐴𝐵𝐶?
Enter the area in the box.
14.5
𝑢𝑛𝑖𝑡𝑠2
Groups 1, 2, and 3
2018 Geometry Bootcamp

59. 2018 Geometry Bootcamp
MAFS.912.G-GPE.2.7
A triangle has vertices at (1, 3), (2, −3), and (−1, −1). What is the approximate perimeter of the triangle? 10 14 15 16
Groups 1, 2, and 3 B
2018 Geometry Bootcamp

60. 2018 Geometry Bootcamp
MAFS.912.G-GPE.2.7
Given the polygon with vertices P(5, -1), Q(-1, -4), R(-3, 1), and S(0, 3). Find the area and the perimeter of PQRS. Round your answer to the nearest tenth.
Enter your answers in the boxes.
Area:
Perimeter:
𝑠𝑞𝑢𝑎𝑟𝑒 𝑢𝑛𝑖𝑡𝑠
𝑢𝑛𝑖𝑡𝑠 29
22.1
Groups 2 and 3
2018 Geometry Bootcamp

61. 2018 Geometry Bootcamp
MAFS.912.G-GPE.2.7
What is the perimeter, in grid units, of a regular octagon that has one side with endpoints (-1, 2) and (3, -1)?
Enter your answer in the box. 40
Groups 2 and 3
2018 Geometry Bootcamp

62. 2018 Geometry Bootcamp
MAFS.912.G-GPE.2.7
What is the exact perimeter of a parallelogram with vertices at 3, 2 , 4,4 , and (6, 1)?
𝟐∙ 𝟏𝟎 +𝟐∙ 𝟓
Groups 2 and 3
2018 Geometry Bootcamp