Question

question
what is the image point of (1, 2) after the transformation $d_2 \circ r_{90^\circ}$?
answer attempt 1 out of 2
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Explanation:

Step1: Rotate the point

When we rotate a point \((x,y)\) by \(90^{\circ}\) counter - clockwise about the origin, the transformation rule is \((x,y)\to(-y,x)\).
For the point \((1,2)\), after \(R_{90}\) (a \(90^{\circ}\) counter - clockwise rotation about the origin), we have \(x = 1\) and \(y=2\).
Using the rotation formula \((x,y)\to(-y,x)\), the new point is \((- 2,1)\).

Step2: Dilate the rotated point

The dilation \(D_{2}\) has a scale factor \(k = 2\). The rule for dilation about the origin is \((x,y)\to(kx,ky)\).
For the point \((-2,1)\) and \(k = 2\), we substitute \(x=-2\) and \(y = 1\) into the dilation formula \((x,y)\to(kx,ky)\).
We get \((2\times(-2),2\times1)=(-4,2)\).

Answer:

\((-4,2)\)