Question

If W(−10,4),X(−3,−1), and Y(−5,11) classify ΔWXY by its sides. Show all work to justify your answer.

WX=
XY=
WY=​

Answer 1

After calculating the sides of ∆WXY, it is determined that WX and WY are equal, and XY is different, classifying ∆WXY as an isosceles triangle.

Step-by-step explanation:

We are tasked with classifying ∆WXY by its sides. To do this, we must calculate the lengths of the sides WX, XY, and WY and determine whether they are all equal, which would make the triangle equilateral, or if they are not equal, which would make the triangle scalene or isosceles.

Let's calculate each side using the distance formula, √((x2-x1)² + (y2-y1)²):

• Length of WX = √((-3 - (-10))² + ((-1) - 4)²) = √(49 + 25) = √74
• Length of XY = √((-5 - (-3))² + (11 - (-1))²) = √(4 + 144) = √148
• Length of WY = √((-5 - (-10))² + (11 - 4)²) = √(25 + 49) = √74

Since WX = WY and both are not equal to XY, ∆WXY is an isosceles triangle.