1. 1. Find a point between A(–3, 5) and B(7, 5).
ANSWER
Sample: (2, 5)
2. Find the average of –11 and 5.
ANSWER –3
3. Solve = 5. 2
x + 7
ANSWER 3
ANSWER
5.48
4. Find √30 to the nearest hundredth.
ANSWER
6.71
5. Find √5 + √20 to the nearest hundredth.

2. Measure Geometric Figures
Target
Measure Geometric Figures
You will…
Find lengths of segments in the coordinate plane.

3. Vocabulary
midpoint – is the point that divides the segment into two congruent segments
segment bisector – is a point, ray, line, line segment, or plane that intersects a segment at its midpoint

4. Vocabulary
Midpoint Formula – If A(x1, y1) and B(x2, y2) are points in a coordinate plane, then the midpoint M of AB has coordinates
x-coordinate of the midpoint
y-coordinate of the midpoint

5. Let M(xm, ym) xm = ym = Vocabulary
Midpoint Formula – Finding an endpoint when the midpoint is known…
Let M(xm, ym)
xm =
ym =

6. Vocabulary
Distance Formula – If A(x1, y1) and B(x2, y2) are points in a coordinate plane, then the distance between A and B is
“change in y”
“change in x”

7. Point T is the midpoint of XY . So, XT = TY = 39.9 cm.
EXAMPLE 1
Find segment lengths
In the skateboard design, VW bisects XY at point T, and XT = 39.9 cm. Find XY.
Skateboard
SOLUTION
Point T is the midpoint of XY . So, XT = TY = 39.9 cm.
XY = XT + TY
Segment Addition Postulate =
Substitute.
= 79.8 cm
Add.

8. Use algebra with segment lengths
EXAMPLE 2
Use algebra with segment lengths
Point M is the midpoint of VW . Find the length of VM .
ALGEBRA
SOLUTION
STEP 1
Write and solve an equation. Use the fact that VM = MW.
VM = MW
Definition of Midpoint
4x – 1 = 3x + 3
Substitute.
x – 1 = 3
Subtract 3x from each side.
x = 4
Add 1 to each side.

9. EXAMPLE 2
Use algebra with segment lengths
STEP 2
Evaluate the expression for VM when x = 4.
VM = 4x – 1 = 4(4) – 1 = 15
So, the length of VM is 15.
Check: Because VM = MW, the length of MW should be 15. If you evaluate the expression for MW, you should find that MW = 15.
MW = 3x + 3 = 3(4) +3 = 15

10. GUIDED PRACTICE
for Examples 1 and 2
In Exercises 1 and 2, identify the segment bisector of PQ . Then find PQ. 1. 3 4
ANSWER
MN; 2.
line l ; 11 5 7
ANSWER

11. EXAMPLE 3
Use the Midpoint Formula
a. FIND MIDPOINT The endpoints of RS are R(1,–3) and S(4, 2). Find the coordinates of the midpoint M.
SOLUTION
a. Use the Midpoint Formula. 2
x1 + x2
y1 + y2 , M
1 + 4 2
– 3 + 2 , M 2 5 M , – 1

12. EXAMPLE 3
Use the Midpoint Formula
b. FIND ENDPOINT The midpoint of JK is M(2, 1). One endpoint is J(1, 4). Find the coordinates of endpoint K.

13. EXAMPLE 3
Use the Midpoint Formula
SOLUTION
FIND ENDPOINT Let (x, y) be the coordinates of endpoint K. Use the Midpoint Formula.
STEP 1
Find x.
STEP 2
Find y.
1+ x 2 =
4+ y 1 2 =
1 + x = 4
4 + y = 2
x = 3
y = – 2
The coordinates of endpoint K are (3, – 2).
ANSWER

14. GUIDED PRACTICE
for Example 3
3. The endpoints of AB are A(1, 2) and B(7, 8). Find the coordinates of the midpoint M.
ANSWER
(4,5)
4. The midpoint of VW is M(– 1, – 2). One endpoint is W(4, 4). Find the coordinates of endpoint V.
ANSWER
(– 6, – 8)

15. EXAMPLE 4
Standardized Test Practice
Use the Distance Formula. You may find it helpful to draw a diagram.
SOLUTION

16. Standardized Test Practice
EXAMPLE 4
Standardized Test Practice
(x – x ) + (y – y ) 2 1 RS =
Distance Formula
[(4 – 2)] + [(–1) –3] 2 =
Substitute.
(2) + (–4 ) 2 =
Subtract.
4+16 =
Evaluate powers. 20 =
Add.
4.47 ~
Use a calculator to approximate the square root.
The correct answer is C.
ANSWER

17. GUIDED PRACTICE for Example 4
5. In Example 4, does it matter which ordered pair you choose to substitute for (x , y ) and which ordered pair you choose to substitute for (x , y )? Explain. 1 2
No, when squaring the differences in the coordinates, you get the same answer as long as you choose the x and y values from the same point.
SAMPLE ANSWER

18. GUIDED PRACTICE
for Example 4
6. What is the approximate length of AB , with endpoints A(–3, 2) and B(1, –4)?
6.1 units
7.2 units
8.5 units
10.0 units B
ANSWER