Question

△abc is shown on the coordinate plane below. what is the perimeter of △abc? if necessary, round your answer to the nearest tenth. units

Explanation:

Step1: Determine the coordinates of points

$A(-6,4)$, $B(8, - 1)$, $C(0,-9)$

Step2: Use the distance - formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ to find the lengths of the sides

For side $AB$:
Let $(x_1,y_1)=(-6,4)$ and $(x_2,y_2)=(8,-1)$
$AB=\sqrt{(8 + 6)^2+(-1 - 4)^2}=\sqrt{16^2+(-5)^2}=\sqrt{256 + 25}=\sqrt{281}\approx16.8$
For side $BC$:
Let $(x_1,y_1)=(8,-1)$ and $(x_2,y_2)=(0,-9)$
$BC=\sqrt{(0 - 8)^2+(-9 + 1)^2}=\sqrt{(-8)^2+(-8)^2}=\sqrt{64+64}=\sqrt{128}\approx11.3$
For side $AC$:
Let $(x_1,y_1)=(-6,4)$ and $(x_2,y_2)=(0,-9)$
$AC=\sqrt{(0 + 6)^2+(-9 - 4)^2}=\sqrt{6^2+(-13)^2}=\sqrt{36 + 169}=\sqrt{205}\approx14.3$

Step3: Calculate the perimeter $P$

$P=AB + BC+AC\approx16.8+11.3 + 14.3=42.4$

Answer:

$42.4$