Question

what is the perimeter of △abc? perimeter = units

Explanation:

Step1: Find length of AB

Points A(-6,4) and B(-2,4). Since y - coordinates are the same, $AB=\vert- 2-(-6)\vert=\vert-2 + 6\vert=4$.

Step2: Find length of BC

Points B(-2,4) and C(-6,-8). Use distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here $x_1=-2,y_1 = 4,x_2=-6,y_2=-8$. Then $BC=\sqrt{(-6+2)^2+(-8 - 4)^2}=\sqrt{(-4)^2+(-12)^2}=\sqrt{16 + 144}=\sqrt{160}=4\sqrt{10}$.

Step3: Find length of AC

Points A(-6,4) and C(-6,-8). Since x - coordinates are the same, $AC=\vert4-(-8)\vert=\vert4 + 8\vert = 12$.

Step4: Calculate perimeter

Perimeter of $\triangle ABC=AB + BC+AC=4+4\sqrt{10}+12=16 + 4\sqrt{10}$.

Answer:

$16 + 4\sqrt{10}$