 # Geometry 1 3 Segments Midpoints and distance formula

• Slides: 13 Geometry 1. 3 Segments, Midpoints and distance formula Essential Question: How can you determine the midpoint between two points? 1. 3 Topic/Objectives • • Know what a bisector is Use the midpoint formula Solve problems with segment bisectors. Use the distance formula Geometry 1. 3 Segment, Midpoints and Distance formula Midpoint A M C • M is the midpoint of segment AC. • M bisects segment AC. • Bisect: divide into two congruent parts. • Congruence marks indicate congruent segments. Geometry 1. 3 Segment, Midpoints and Distance formula A Segment Bisector can be a… segment ray line Plane Geometry 1. 3 Segment, Midpoints and Distance formula Midpoint Formula M (x 2, y 2) The midpoint is the average point. (x 1, y 1) Geometry 1. 3 Segment, Midpoints and Distance formula Midpoint Example Find the midpoint of segment AB if A is point (10, -6) and B is point (2, 8). Solution: (6, 1) Geometry 1. 3 Segment, Midpoints and Distance formula Your Turn Find the midpoint of the segment between (20, -14) and (-16, 4). Solution: (2, -5) Geometry 1. 3 Segment, Midpoints and Distance formula Another midpoint problem The midpoint of segment DH is O(3, 4). One endpoint is D(5, 7). Find the coordinates of H. D(5, 7) Write out the formula: O(3, 4) H(x, y) continues… Geometry 1. 3 Segment, Midpoints and Distance formula midpoint problem continued There are two equations to solve: Solve: continues… Geometry 1. 3 Segment, Midpoints and Distance formula midpoint problem continued Since x = 1 and y = 1, the other endpoint is H(1, 1). D(5, 7) O(3, 4) H(1, 1) Geometry 1. 3 Segment, Midpoints and Distance formula Your Turn The midpoint of segment AB is M(1, 5). If one endpoint is A(-3, -4), find the coordinates of B. Solution: is the midpoint. Solve for y: Solve for x: Endpoint (5, 14) Geometry 1. 3 Segment, Midpoints and Distance formula Distance Formula Geometry 1. 3 Segment, Midpoints and Distance formula EX: Find distance between R and S. Round to nearest tenth if needed. Geometry 1. 3 Segment, Midpoints and Distance formula