Question

pentagon abcde is dilated according to the rule do.3(x,y) to create the image pentagon abcde, which is shown on the graph. what are the coordinates of point a of the pre - image? (-1,1) (-1,2) (-9,6) (-9,18)

Explanation:

Step1: Recall the dilation formula

The dilation rule is \(D_{0,3}(x,y)=(0.3x,0.3y)\). Let the coordinates of point \(A\) (pre - image) be \((x,y)\) and the coordinates of point \(A'\) (image) be \((x',y')\). Then \(x' = 0.3x\) and \(y'=0.3y\).

Step2: Find the coordinates of \(A'\) from the graph

From the graph, the coordinates of \(A'\) are \((- 3,1.8)\).

Step3: Solve for \(x\) and \(y\)

Since \(x'=0.3x\) and \(x'=-3\), then \(x=\frac{x'}{0.3}=\frac{-3}{0.3}=-9\).
Since \(y' = 0.3y\) and \(y'=1.8\), then \(y=\frac{y'}{0.3}=\frac{1.8}{0.3}=6\).

Answer:

\((-9,6)\)