Finding the Midpoint of a Line Segment a.) Graph where points A and B are shown. b.) Explain how to bisect, that means divide into two congruent line segments. Use that to find the midpoint M of . c) What are the coordinates of midpoint M? d.) Compare the x coordinates of A, B and M. Compare the y coordinates of A, B and M. How are the coordinates of midpoint M related to the coordinates of A and B?

A (3,4) B (-5,-2)

Daily Warm-Up Rewrite each statement Symbolically. Segment AB Length of Segment AB Ray BA Line Segment CD Segment CD is Congruent to Segment AB Length of Segment AB is the same as the length of CD. Find the missing length 7. What is the Length of AB . 3x-4 -15x-8 A B C

1.3 Using Midpoint and Distance Formulas

Core Concepts The midpoint of a segment is the point that divides the segment into two congruent segments. A segment bisector is a point, ray, line, line segment or plane that intersects the segment at it’s midpoint C A M B D

Example 1 In the skateboard design YA BISECTS EH at point R, and ER is 14 inches. Find EH. Use the Segment Addition Postulate. ER + RH = EH 14 + 14 = 28 EH = 28 inches Y R A E

You Try! Identify the segment bisector of WE. Then find the length of WE. E 7.5 L H W

Example 2 Point M is the midpoint of VW. Find the length of VM. 4x - 1

You try! Identify the segment bisector of PQ and then find MQ. 11 - 2x

Core Concepts Midpoint Formula is the average of the x values and the average of the y values of the endpoints.

Example 3 a.) The endpoints of RS are R(1,-3) and S(4, 2), Find the coordinates of the midpoint. S(4, 2) R(1,-3)

b. ) The midpoint of JK is M(2, 1). One endpoint is J(1,4) b.) The midpoint of JK is M(2, 1). One endpoint is J(1,4). Find the coordinates of endpoint K. Use the midpoint formula and substitute what you know.

You try! The endpoints of AB are A(-4,3) and B(-6,5) Find the coordinates of the midpoint M. The midpoint of TU is M(2,4). One endpoint is T(1,1). Find the other endpoint.

Core Concepts On a Coordinate Plane, to find the distance (or length) of a segment, AB, that is NOT horizontal nor vertical, You can USE: Pythagorean Theorem Use the Distance Formula D= On a Coordinate Plane, to find the distance (or length) of a segment, AB, that is NOT horizontal nor vertical, You can USE: Pythagorean Theorem Use the Distance Formula D= On a Coordinate Plane, to find the distance (or length) of a segment, AB, that is NOT horizontal nor vertical, You can USE: Pythagorean Theorem Use the Distance Formula D=

Example 4 Your school is 4 miles east and one mile south of your apartment. A recycling center, where your class is going on a field trip, is 2 miles east and 3 miles north of your apartment. Estimate the distance of the recycling center and your school. RS= RS =

You try!! In example 4, a park is 3 miles east and 4 miles south of your apartment. Find the distance between the park and your school.