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**Lesson 1.3 Distance and Midpoints**

Geometry CP Mrs. Mongold

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Chapter 1 Foldable Flap 2 Distance Formulas Number Line -3 4 P Q

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**Chapter 1 Foldable Flap 2 Distance Formulas Cont… Coordinate Plane**

The distance d between two points with coordinates and

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Distance Examples Number Line Use the number line to find QR

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**Answer The coordinates of Q and R are –6 and –3.**

QR = | –6 – (–3) | Distance Formula = | –3 | or 3 Simplify.

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**Another Number Line Example**

Use the number line to find AX

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**Answer The coordinates of A and X are -5 and 3**

AX = |-5 – 3| Distance Formula AX = |-8| AX = 8

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**More Distance Examples**

Coordinate Plane Find the distance between E and F

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

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Another Example Find the distance between A and M

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

Label (-3, 4) and (1, 2), and

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**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

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**Chapter 1 Foldable Flap 3 Coordinate Plane**

The coordinates of the midpoint of a segment with endpoints that have coordinates and

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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.

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Answer Coordinate of the midpoint of YO is -4

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

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Answers

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

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Answers (-5, -3)

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**What about working backwards?**

Find the coordinates of D if E(-6, 4) is the midpoint of segment DF and F(-5, -3)

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**Answer Let D be Let E be for the midpoint Let F be So…..**

The coordinates for point D are (-7, 11)

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

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Answer If Q is the midpoint then segments PQ and QR are both equal to 6 – 3x So, 2(6 – 3x) = 14x + 2 12 – 6x = 14x + 2 10 = 20x x = ½ PR = 14(1/2) + 2 = = 9

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

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

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

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