Question

Use the given coordinates to classify the triangle and find its perimeter.S(1, - 6), A (6, – 6), U (3, - 2)

Answer 1

1) Firstly, we'll need to find the length of all legs. We'll use the distance formula derived from the Pythagorean Theorem

`\begin{gathered} d_(SA)=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ d_(SA)=\sqrt[]{(6-1)^2+(-6+6)^2}=5 \\ d_(AU)=\sqrt[]{(3-6)^2+(-2+6)^2}=5 \\ d_(SU)=\sqrt[]{(3-1)^2+(-2+6)^2}=2\sqrt[]{5} \end{gathered}`

Since an isosceles triangle has at least 2 congruent sides then this is an Isosceles Triangle.

2) The Perimeter (2P) is the sum of all sides' length of a polygon. Hence

`\begin{gathered} 2P\text{ =5+5+2}\sqrt[]{5} \\ 2P=10+2\sqrt[]{5} \end{gathered}`

3) So the answer is Isosceles Triangle and 2P =10+2√5