Question

trapezoid defg is dilated according to the rule do.4(x,y) to form the image trapezoid defg, which is shown on the graph. what are the coordinates of point g of the pre - image? (-2,1) (-4,2) (-12,0) (-32,16)

Explanation:

Step1: Recall the dilation formula

If a point \((x,y)\) is dilated by a scale factor \(k\) with center at the origin \((0,0)\), the formula is \((x',y')=(kx,ky)\). Here \(k = 0.4\), and we want to find \((x,y)\) given \((x',y')\). So \(x=\frac{x'}{k}\) and \(y=\frac{y'}{k}\).

Step2: Identify the coordinates of \(G'\)

From the graph, the coordinates of \(G'\) are \((- 4.8,0.8)\).

Step3: Calculate the coordinates of \(G\)

Since \(k = 0.4\), for the \(x\) - coordinate: \(x=\frac{-4.8}{0.4}=-12\), for the \(y\) - coordinate: \(y=\frac{0.8}{0.4} = 0\)

Answer:

\((-12,0)\)