Lesson 1 – 3 Distance and Midpoints Geometry Lesson 1 – 3 Distance and Midpoints Objective: Find the distance between two points. Find the midpoint of a segment.

Distance: on a number line Distance formula (on a number line) The absolute value of the difference between their points.

Use the number line to find the following AC CF FB

Distance: On the coordinate plane Distance formula (on a coordinate plane)

Example Find the distance between C (-4, -6) & D(5, -1) Doesn't matter in which order You subtract x’s or y’s. Radical is already simplified. Write answer as both radical and decimal

Find the distance E (-5, 6) & F (8, -4) J (4, 3) & K (-3, -7)

Midpoint: On a number line Midpoint is the point halfway between the endpoints of the segment. Take the average of the numbers or just add up the numbers divide by 2.

Example Find the midpoint between 15 inches and 37.5 inches.

Example The temperature on a thermometer dropped from a reading of 25 degrees to -8 degrees. Find the midpoint of these temperatures. M = (25 – 8) / 2 M = 17 / 2 M = 8.5 degrees

Midpoint: On coordinate plane Average of both the x’s and y’s

Example Find the coordinates of M, the midpoint of ST, for S (-6, 3) & T (1, 0). Make a visual (helpful for later) S (-6,3) M (? , ?) T (1, 0)

Example Find the midpoint A (5, 12) B(-4, 8) C (-8, -2) D (5, 1)

Find the coordinate of the endpoint Find the coordinates of J, if K (-1, 2) is the midpoint of JL and L (3, -5). Make a visual J (?, ?) K (-1, 2) L (3, -5) K is the midpoint so when I add the x’s and / 2 should = -1 J (-5, 9) (2) (2) (2) (2) Check it: (-5 + 3) / 2 = -1 (9 – 5) / 2 = 2 x + 3 = -2 y – 5 = 4 x = -5 y = 9

Find the Endpoint G (-2, 14) y = 14 x = -2 Find the coordinates of the missing endpoint if P is the midpoint of EG. E (-8, 6), P (-5, 10) E (-8, 6) P (-5, 10) G (x, y) G (-2, 14) 6 + y = 20 -8 + x = -10 y = 14 x = -2

Example Find the coordinates of the missing endpoint if P is the midpoint of EG. P (-1, 3), E (5, 6) G (-7, 0) x + 5 = -2 y + 6 = 6 y = 0 x = -7

Find the measure PQ = 9y – 2 = 9(4) – 2 = 34 Find the measure of PQ if Q is the midpoint of PR. 9y – 2 = 14 + 5y 4y – 2 = 14 4y = 16 y = 4 PQ = 9y – 2 = 9(4) – 2 = 34

Your Turn Find the measure of YZ if Y is the midpoint of XZ and XY = 2x – 3 and YZ = 27 – 4x 2x – 3 = 27 – 4x 6x – 3 = 27 6x = 30 x = 5 YZ = 27 – 4(5) = 27 – 20 = 7

Your Turn 2(4x + 5) = 78 or 4x + 5 = 78/2 4x + 5 = 39 4x = 34 Find the value of x if C is the midpoint of AB, AC = 4x + 5 and AB = 78. 2(4x + 5) = 78 or 4x + 5 = 78/2 **AB is the whole segment 4x + 5 = 39 4x = 34 x = 8.5

Bisector Segment bisector Any segment, line, or plane that intersects a segment at its midpoint