Question

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

Answer 1

Answer:

The perimeter is 24 units

Step-by-step 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:

$P = AB + BC + AC$

$P =8 + 6 + 10$

$P =24$