Question

1. triangle wxy with vertices w(-4, 8), x(10, 0), and y(-2, -8): k = 1/4

Explanation:

Step1: Apply dilation formula

For a point \((x,y)\) and scale factor \(k\), the dilated point is \((kx,ky)\).

Step2: Find \(W'\)

Given \(W(-4,8)\) and \(k = \frac{1}{4}\).
\(x=-4,y = 8,k=\frac{1}{4}\)
\(W'=(\frac{1}{4}\times(-4),\frac{1}{4}\times8)=(-1,2)\)

Step3: Find \(X'\)

Given \(X(10,0)\) and \(k=\frac{1}{4}\)
\(x = 10,y=0,k=\frac{1}{4}\)
\(X'=(\frac{1}{4}\times10,\frac{1}{4}\times0)=(\frac{5}{2},0)\)

Step4: Find \(Y'\)

Given \(Y(-2,-8)\) and \(k=\frac{1}{4}\)
\(x=-2,y=-8,k=\frac{1}{4}\)
\(Y'=(\frac{1}{4}\times(-2),\frac{1}{4}\times(-8))=(-\frac{1}{2},-2)\)

Answer:

\(W'(-1,2)\)
\(X'(\frac{5}{2},0)\)
\(Y'(-\frac{1}{2},-2)\)