13 1 Distance and Midpoint Formulas Goal Find

13. 1 Distance and Midpoint Formulas Goal: Find the distance between and midpoint of two points.

Warm-up You deposit $300 into an account that pays 2% interest, compounded daily. How much money is in the account after one year? What is the simplest form of 1/20/2022 ? 2

The Distance Formula The distance formula gives the distance d between two points (x 1, y 1) and (x 2, y 2). 1/20/2022 3

Example Find the distance between the two points. 1. (0, 0) and (-5, 12) 1/20/2022 2. (-4, 4) and (5, -4) 4

Example Scalene: No sides congruent Isosceles: 2 sides congruent Equilateral: All sides congruent Classify ΔABC as scalene, isosceles, or equilateral. Since none of the sides have the same length ΔABC is scalene. 1/20/2022 5

Midpoint The midpoint is the point on a segment that is equidistant from the two endpoints. Midpoint Formula The midpoint formula gives the midpoint M of the line segment joining A(x 1, y 1) and B(x 2, y 2). A(x 1, y 1) Midpoint M B(x 2, y 2) 1/20/2022 6

Example Find the midpoint of the line segment joining the two points. 1. (0, 0) and (-4, 6) 2. (-8, 1) and (3, -3) 1/20/2022 7

Example Write the equation for the perpendicular bisector of the line segment joining (-2, 0) and (6, 4). A perpendicular bisector is a line that cuts a segment into 2 congruent segments and forms 4 right angles. (It passes through the segment’s midpoint) A perpendicular has a slope that is the opposite reciprocal. 1/20/2022 8

Example Write the equation for the perpendicular bisector of the line segment joining (-3, -5) and (-7, -9). 1/20/2022 9

Assignment Thatquiz. org 1/20/2022 10