12.4 The Distance Formula

Objectives: Use the distance formula to find the distance between 2 points in a coordinate plane. Determine whether a triangle is a right triangle. Apply the midpoint formula.

Standard Addressed: 2.1.11.A Use operations.

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Ex. 1

Ex. 1 C. (4, 5) and (-5, 7)

•9.22

Ex. 2

Ex. 2b. Given vertices P(-1, -2), Q (5, 2), and R (-3, 1), determine whether triangle PQR is a right triangle.

•Right Triangle

Ex. 3

•3 + 11 , 8 + 2 2 2(7, 5)

Ex. 4a. The center M (3, 4). If one endpoint of a diameter is A (-4, 6), what is the other endpoint, B (x2, y2)?

•3 = x + (-4) 2

6 = -4 + x

X = 10

4 = y + 6 28 = y + 6

y = 2

(10, 2)

Ex. 4b. If the center of a circle is M(-1, -2) and one endpoint of a diameter is A(4, 3), what is the other endpoint, B (x2, y2)?

•-1 = x + 4 2

-2 = 4 + x

X = -6

-2 = y + 3 2-4 = 3 + y

y = -7

(-6, -7)