Question

∆ABC has A(-3, 6), B(2, 1), and C(9, 5) as its vertices. The length of side AB is units. The length of side BC is units. The length of side AC is units. °.

Answer 1

AB = 7.07 units

BC = 8.06 units

AC = 12.04 units

Explanation:

To find the length for each side of the triangle, apply the distance formula between each pair of vertices.

AB

`d = √((x_2-x_1)^2 + (y_2-y_1)^2) \\d = √((2--3)^2 + (1-6)^2) \\d = √((5)^2 + (-5)^2) \\d = √(25 + 25) \\d = √(50) \\d=7.07`

BC

`d = √((x_2-x_1)^2 + (y_2-y_1)^2) \\d = √((9-2)^2 + (5-1)^2) \\d = √((7)^2 + (4)^2) \\d = √(49 + 16) \\d = √(65) \\d=8.06`

AC

`d = √((x_2-x_1)^2 + (y_2-y_1)^2) \\d = √((9--3)^2 + (5-6)^2) \\d = √((12)^2 + (-1)^2) \\d = √(144 + 1) \\d = √(145) \\d=12.04`