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Lesson 1.3 Distance and Midpoints Geometry CP Mrs. Mongold.

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Presentation on theme: "Lesson 1.3 Distance and Midpoints Geometry CP Mrs. Mongold."— Presentation transcript:

1 Lesson 1.3 Distance and Midpoints Geometry CP Mrs. Mongold

2 Chapter 1 Foldable Flap 2 Distance Formulas –Number Line PQ -34

3 Chapter 1 Foldable Flap 2 Distance Formulas Cont… –Coordinate Plane The distance d between two points with coordinates and

4 Distance Examples Number Line –Use the number line to find QR

5 Answer The coordinates of Q and R are –6 and –3. QR= | –6 – (–3) |Distance Formula = | –3 | or 3Simplify.

6 Another Number Line Example Use the number line to find AX

7 Answer The coordinates of A and X are -5 and 3 AX = |-5 – 3| Distance Formula AX = |-8| AX = 8

8 More Distance Examples Coordinate Plane Find the distance between E and F

9 Answer The coordinates are E(-4, 1) and F(3, -1) Label them

10 Another Example Find the distance between A and M

11 Answer The coordinates are A(-3, 4) and M(1, 2) Label (-3, 4) and (1, 2), and

12 Chapter 1 Foldable Flap 3 Midpoint Formulas –Number Line The coordinate of the midpoint of a segment with endpoints that have coordinates a and b is

13 Chapter 1 Foldable Flap 3 Coordinate Plane –The coordinates of the midpoint of a segment with endpoints that have coordinates and

14 Midpoint Examples The coordinates on a number line Y and O are 7 and -15 respectively. Find the coordinate of the midpoint of segment YO.

15 Answer Coordinate of the midpoint of YO is -4

16 More Examples Find the coordinates of M, the midpoint of segment GH for G(8, -6) and H (-14, 12)

17 Answers

18 More Examples Find the coordinates of the midpoint of segment XY if X(-2, 3) and Y(-8, -9)

19 Answers (-5, -3)

20 What about working backwards? Find the coordinates of D if E(-6, 4) is the midpoint of segment DF and F(-5, -3)

21 Answer Let D be Let E be for the midpoint Let F be So….. The coordinates for point D are (-7, 11)

22 More Examples What is the measure of segment PR if Q is the midpoint of segment PR?

23 Answer If Q is the midpoint then segments PQ and QR are both equal to 6 – 3x So, 2(6 – 3x) = 14x – 6x = 14x = 20x x = ½ PR = 14(1/2) + 2 = = 9

24 Last Example What is the measure of segment AC if B is the midpoint of segment AC?

25 Answer 2(2a – 1) = 3a + 1 4a – 2 = 3a + 1 a = 3 AC = 3(3) + 1 AC = 10

26 Ticket Out The Door Find the distance and midpoint of segment AB for A(5, 12) and B(-4, 8)


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