Question

what is the image point of (-4,6) after the transformation $r_{y=-x} \circ d_3$?
answer attempt 1 out of 2
( 12, -18 ) submit answer

Explanation:

Step1: Dilation

First, perform the dilation \(D_{\frac{3}{1}}\). For a point \((x,y)\), dilation with scale factor \(k = 3\) gives \((kx,ky)\).
For the point \((- 4,6)\), after dilation \(D_{3}\), we have \((-4\times3,6\times3)=(-12,18)\).

Step2: Reflection

Next, perform the reflection \(r_{y =-x}\). The rule for reflection over the line \(y=-x\) is \((x,y)\to(-y,-x)\).
For the point \((-12,18)\), after reflection \(r_{y=-x}\), we substitute \(x=-12\) and \(y = 18\) into the rule: \((-18,12)\).

Answer:

\((12,-18)\)