Question

If W (-10,4),X(-3,-1)and Y (-5,11) classify angle WXY by its sides

Answer 1

So,

Let me graph the three points here below:

To classify this triangle by its sides, the first thing we need to do is to find the measure of each segment. For this, we could use the formula for the distance between two points for each one.

Let's start with segment WX.

`\begin{gathered} WX=\sqrt[]{(4-(-1))^2+(-10-(-3))^2} \\ WX=\sqrt[]{(5^2)+(-7)^2} \\ WX=\sqrt[]{25+49} \\ WX=\sqrt[]{74} \end{gathered}`

Now, continue with XY:

`\begin{gathered} XY=\sqrt[]{(11-(-1))^2+(-5-(-3))^2} \\ XY=\sqrt[]{12^2+(-2)^2} \\ XY=\sqrt[]{148} \end{gathered}`

And finally, WY:

`\begin{gathered} WY=\sqrt[]{(11-4)^2+(-5-(-10))^2} \\ WY=\sqrt[]{7^2+5^2} \\ WY=\sqrt[]{74} \end{gathered}`

As you can see, sides WY and WX are equal. So, the triangle has two equal sides and one different.

For this reason, the triangle is an isosceles triangle.