Question

A triangle has vertices at (-9,2), (-9,-6), (-3,-6). What is the perimiter of the triangle in units?

Answer 1

The perimeter is 24 units

Explanation:

Given

`A = (-9,2)` ---
`(x_1,y_1)`

`B = (-9,-6)` ---
`(x_2,y_2)`

`C = (-3,-6)` ---
`(x_3,y_3)`

Required

Determine the perimeter

To do this, we calculate the distance AB, BC and AC.

Distance is calculated as:

`d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2`

So, we have:

`AB = \sqrt{(-9 - -9)^2 + (2 - -6)^2`

`AB = \sqrt{64`

`AB = 8`

`BC = \sqrt{(-9 - -3)^2 + (-6 - -6)^2`

`BC = \sqrt{36`

`BC = 6`

`AC = \sqrt{(-9 --3)^2 + (2 --6)^2`

`AC = \sqrt{100`

`AC = 10`

So, the perimeter (P) is:

`P = AB + BC + AC`

`P =8 + 6 + 10`

`P =24`