Do now Write your comparison on the Do Now Sheet.

Section 1.3-Use midpoint and distance formulas Geometry

Vocabulary Segment bisector: a point, ray, line, line segment, or plane that intersects the segment at its midpoint Midpoint: point that divides the segment into two congruent segments

Example 1 In the skateboard design, VW bisects XY at point T, and XT = 39.9 cm. Find XY. Skateboard Point T is the midpoint of XY . So, XT = TY = 39.9 cm. XY = XT + TY = 39.9 + 39.9 = 79.8 cm

Point M is the midpoint of VW . Find the length of VM . Example 2 Point M is the midpoint of VW . Find the length of VM . STEP 1: Write and solve an equation. Use the fact that VM = MW. STEP 2: Evaluate the expression for VM when x = 4. VM = 4x – 1 = 4(4) – 1 = 15 VM = MW 4x – 1 = 3x + 3 So, the length of VM is 15. x – 1 = 3 *** Do a mental check for MW. x = 4

The midpoint formula If 𝐴 𝑥 1 , 𝑦 1 and B 𝑥 2 , 𝑦 2 are points in a coordinate plane, then the midpoint M of 𝐴𝐵 has coordinates 𝑥 1 + 𝑥 2 2 , 𝑦 1 + 𝑦 2 2 .

Example 3 (a) The coordinates of the midpoint M are 𝟓 𝟐 ,− 𝟏 𝟐 . a. FIND MIDPOINT The endpoints of RS are R(1,–3) and S(4, 2). Find the coordinates of the midpoint M. 2 5 1 + 4 – 3 + 2 = , M – 1 The coordinates of the midpoint M are 𝟓 𝟐 ,− 𝟏 𝟐 .

Example 3 (b) STEP 1 Find x. STEP 2 Find y. 1+ x 2 = 4+ y 1 2 = b. FIND ENDPOINT The midpoint of JK is M(2, 1). One endpoint is J(1, 4). Find the coordinates of endpoint K. STEP 1 Find x. STEP 2 Find y. 1+ x 2 = 4+ y 1 2 = 1 + x = 4 4 + y = 2 x = 3 y = – 2 The coordinates of endpoint K are (3, – 2).

The distance formula If 𝐴 𝑥 1 , 𝑦 1 and 𝐵 𝑥 2 , 𝑦 2 are points in a coordinate plane, then the distance between A and B is 𝐴𝐵= 𝑥 2 − 𝑥 1 2 + 𝑦 2 − 𝑦 1 2 .

Example 4-Standardized test prep Use the distance formula

Example 4 continued 𝑅𝑆= 𝑥 2 − 𝑥 1 2 + 𝑦 2 − 𝑦 1 2 = 4−2 2 + −1−3 2 𝑅𝑆= 𝑥 2 − 𝑥 1 2 + 𝑦 2 − 𝑦 1 2 = 4−2 2 + −1−3 2 = 2 2 + (−4) 2 = 4+16 = 20 ≈4.47 The correct answer is C.

Homework Textbook pages 19-20 # 5, 9, 12, 20, 23, 25, 32, 34