Lesson 1 3 Distance and Midpoints Geometry CP

Lesson 1. 3 Distance and Midpoints Geometry CP Mrs. Mongold

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

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

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

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

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

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

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

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

Another Example • Find the distance between A and M

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

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

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

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.

Answer Coordinate of the midpoint of YO is -4

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

Answers

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

Answers • (-5, -3)

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

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

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

Answer • If Q is the midpoint then segments PQ and QR are both equal to 6 – 3 x • So, 2(6 – 3 x) = 14 x + 2 12 – 6 x = 14 x + 2 10 = 20 x x=½ PR = 14(1/2) + 2 = 7 + 2 = 9

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

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

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