Given:
The point is (-12,-8).
Rule of transformation is [tex]R_{270^\circ}\circ D_{\dfrac{1}{4}}[/tex].
To find:
The coordinates of image after transformation.
Solution:
According to the rule of transformation [tex]R_{270^\circ}\circ D_{\dfrac{1}{4}}[/tex], first the point is dilated by factor [tex]\dfrac{1}{4}[/tex] with origin as center of dilation after that it was rotated 270 degrees anticlockwise.
If a point is dilated by factor [tex]\dfrac{1}{4}[/tex] with origin as center of dilation, then
[tex](x,y)\to \left(\dfrac{1}{4}x,\dfrac{1}{4}y\right)[/tex]
[tex](-12,-8)\to \left(\dfrac{1}{4}(-12),\dfrac{1}{4}(-8)\right)[/tex]
[tex](-12,-8)\to \left(-3,-2\right)[/tex]
If a point is rotated 270 degrees anticlockwise, then
[tex](x,y)\to (y,-x)[/tex]
[tex](-3,-2)\to ((-2),-(-3))[/tex]
[tex](-3,-2)\to (-2,3)[/tex]
Therefore, the coordinates of image after transformation are (-2,3).
