Question

What is the perimeter of the triangle shown on the coordinate plane, to the nearest tenth of a unit?


A. 19.2 units

B. 22.3 units

C. 27.4 units

D. 36.0 units

Answer 1

its is 27.4 units just square it out 

Answer 2

ANSWER

The correct answer is C

EXPLANATION

We use the distance formula to determine the length of each side and add them.

The vertices of the triangle has coordinates $B(-1,7)$,  $C(6,3)$ and  $B(-4,-1)$.

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

$|AB|=\sqrt{(-1--4)^2+(7--1)^2}$

$|AB|=\sqrt{(-1+4)^2+(7+1)^2}$

$|AB|=\sqrt{(3)^2+(8)^2}$

$|AB|=\sqrt{9+64}$

$|AB|=\sqrt{73}$

$|AB|=8.54$ units

$|BC|=\sqrt{(-1-6)^2+(7-3)^2}$

$|BC|=\sqrt{(-7)^2+(4)^2}$

$|BC|=\sqrt{49+16}$

$|BC|=\sqrt{65}$

$|BC|=8.06$ units

$|AC|=\sqrt{(-4-6)^2+(-1-3)^2}$

$|AC|=\sqrt{(-10)^2+(-4)^2}$

$|AC|=\sqrt{100+16}$

$|AC|=\sqrt{116}$

$|AC|=10.77$ units

$Perimeter=|AC|+|BC|+|AB|$

$Perimeter=10.77+8.06+8.54$

$Perimeter=27.4$ units