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 \(W(-10,4)\) and \(X(-3,-1)\):
\(d_{WX}=\sqrt{(-3+10)^2+(-1 - 4)^2}=\sqrt{7^2+(-5)^2}=\sqrt{49 + 25}=\sqrt{74}\)
For \(X(-3,-1)\) and \(Y(-5,11)\):
\(d_{XY}=\sqrt{(-5 + 3)^2+(11+1)^2}=\sqrt{(-2)^2+12^2}=\sqrt{4+144}=\sqrt{148}=2\sqrt{37}\)
For \(Y(-5,11)\) and \(W(-10,4)\):
\(d_{YW}=\sqrt{(-10 + 5)^2+(4-11)^2}=\sqrt{(-5)^2+(-7)^2}=\sqrt{25 + 49}=\sqrt{74}\)

Step2: Classify the triangle

Since \(d_{WX}=\sqrt{74}\), \(d_{YW}=\sqrt{74}\) and \(d_{XY}=2\sqrt{37}\), two sides are equal (\(WX = YW\))

Answer:

The lengths of the sides are \(WX=\sqrt{74}\), \(XY = 2\sqrt{37}\), \(YW=\sqrt{74}\). \(\triangle WXY\) is an isosceles triangle.