Lesson 1.3 Distance and Midpoints

Distance Formula Number Line -3 4 P Q

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

Midpoint Formula Number Line The coordinate of the midpoint of a segment with endpoints that have coordinates a and b is

Midpoint Cont. 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 for the midpoint Let F be So….. 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 – 3x So, 2(6 – 3x) = 14x + 2 12 – 6x = 14x + 2 10 = 20x 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(2a – 1) = 3a + 1 4a – 2 = 3a + 1 a = 3 AC = 3(3) + 1 AC = 10