Question

1. if w(-10,4), x(-3,-1), and y(-5,11). find the length of each side and classify △wxy by its sides.

Explanation:

Step1: Use the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
For side \(WX\):
\(x_1=-10,y_1 = 4,x_2=-3,y_2=-1\)
\(WX=\sqrt{(-3+10)^2+(-1 - 4)^2}=\sqrt{7^2+(-5)^2}=\sqrt{49 + 25}=\sqrt{74}\)

Step2: For side \(XY\)

\(x_1=-3,y_1=-1,x_2=-5,y_2 = 11\)
\(XY=\sqrt{(-5 + 3)^2+(11+1)^2}=\sqrt{(-2)^2+12^2}=\sqrt{4+144}=\sqrt{148}=2\sqrt{37}\)

Step3: For side \(WY\)

\(x_1=-10,y_1 = 4,x_2=-5,y_2 = 11\)
\(WY=\sqrt{(-5 + 10)^2+(11 - 4)^2}=\sqrt{5^2+7^2}=\sqrt{25+49}=\sqrt{74}\)

Answer:

Since \(WX=\sqrt{74}\), \(XY = 2\sqrt{37}\), \(WY=\sqrt{74}\), two sides (\(WX\) and \(WY\)) are equal. So, \(\triangle WXY\) is an isosceles triangle.