Question

question
what is the image point of $(0,-6)$ after the transformation $d_{\frac{1}{2}}\circ r_{y = -x}$?
answer attempt 2 out of 2
$(-3,0)$ submit answer

Explanation:

Step1: Find the image after reflection

The rule for reflection over the line \(y = -x\) is \((x,y)\to(-y,-x)\).
For the point \((0,-6)\), substituting \(x = 0\) and \(y=-6\) into the rule: \((0,-6)\to(6,0)\)

Step2: Find the image after dilation

The rule for dilation \(D_{\frac{1}{2}}\) (a dilation with scale factor \(k=\frac{1}{2}\)) is \((x,y)\to(\frac{1}{2}x,\frac{1}{2}y)\)
For the point \((6,0)\), substituting \(x = 6\) and \(y = 0\) into the rule: \((6,0)\to(\frac{1}{2}\times6,\frac{1}{2}\times0)=(3,0)\)

Answer:

\((3,0)\)