Answer to Question #113350 in Analytic Geometry for Amber

Question

What is the perimeter of △TUV?
Write your answer as an integer or as a decimal rounded to the nearest tenth.
Perimeter=
units
the coordinate points are T(-7,-9) V(3,10) U(6,-7)

Answer 1

Explanation

• The formula of the distance.

$\qquad\qquad \small |AB| = \sqrt{(x_2-x_1)^2 + (y_2- y_1)^2}$

• And the calculation of the lengths of the 3 sides is done using it.

Calculations

$\qquad \begin{aligned} \small \text{Perimeter}\, &= \small |TU|+|UV|+|VT|\\ &= \small \sqrt{(-7-6)^2+(-9+7)^2} +\\+ \small \sqrt{(6-3)^2+(-7-10)^2} +\\+ \small \sqrt{(3+7)^2+(10+9)^2}\\ &= \small \bold{51.89 \,units}\\ &\approx \small \bold{52 \,units} \end{aligned}$