Welcome to Interactive Chalkboard 1.3 Distance and Midpoints Learning Goals: Students will compute segment lengths using midpoints and segment bisectors. Students will use the Midpoint Formula to find the midpoint of a line segment. Students will use the Distance Formula or Pythagorean Theorem to find the distance of a line segment.

Number Line & Coordinate Plane PQ = I b – a I or I a – b I Coordinate Plane The distance d between two points with coordinates 𝑥 1 , 𝑦 1 & 𝑥 2 , 𝑦 2 is given by d = 𝑥 1 − 𝑥 2 2 + 𝑦 1 − 𝑦 2 2

Use the number line to find QR. Example 1: Use the number line to find QR. Use the number line to find AX. Example 3-1a

Example 2: A. Find the distance between (-4,1) & (3,-1) using distance formula B. Find the distance. Example 3-2c

Midpoint Segment Bisector The midpoint of a segment is the point halfway between the endpoints of the segment. Coordinate Plane 𝑀= 𝑥 1 + 𝑥 2 2 , 𝑦 1 + 𝑦 2 2 Segment Bisector Any segment, line, or plane that intersects a segment at its midpoint is called a segment bisector.

Example 3: Find the coordinates of M, the midpoint of , for G(8, –6) and H(–14, 12). Find the coordinates of the midpoint of for X(–2, 3) and Y(–8, –9). Example 3-3b

Example 4: Find the coordinates of D if E(–6, 4) is the midpoint of and F has coordinates (–5, –3). Example 5: If 𝑅𝑇 is a segment bisector, find the measure of 𝐶𝑂 . R 5x -3 11-2x C O T Example 3-4a

Homework Pg. 24-25 #7-9, 15, 17, 19, 21, 23-28 GRAPH Paper located on table in yellow file holder