Question

find the approximate perimeter of △abc plotted below. a(-4,1) b(-2,3) c(3,-4) choose 1 answer:

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Calculate length of $AB$

For points $A(-4,1)$ and $B(-2,3)$, $x_1=-4,y_1 = 1,x_2=-2,y_2 = 3$.
$AB=\sqrt{(-2-(-4))^2+(3 - 1)^2}=\sqrt{(2)^2+(2)^2}=\sqrt{4 + 4}=\sqrt{8}\approx2.83$.

Step3: Calculate length of $BC$

For points $B(-2,3)$ and $C(3,-4)$, $x_1=-2,y_1 = 3,x_2=3,y_2=-4$.
$BC=\sqrt{(3-(-2))^2+(-4 - 3)^2}=\sqrt{(5)^2+(-7)^2}=\sqrt{25 + 49}=\sqrt{74}\approx8.60$.

Step4: Calculate length of $AC$

For points $A(-4,1)$ and $C(3,-4)$, $x_1=-4,y_1 = 1,x_2=3,y_2=-4$.
$AC=\sqrt{(3-(-4))^2+(-4 - 1)^2}=\sqrt{(7)^2+(-5)^2}=\sqrt{49+25}=\sqrt{74}\approx8.60$.

Step5: Calculate perimeter

Perimeter $P=AB + BC+AC\approx2.83+8.60 + 8.60=20.03\approx20.0$.

Answer:

A. 20.0