Question

What is the image point of (-12, -8) after the transformation R270° 0 D. ?

Answer 1

Answer: -2,3

Step-by-step explanation:

Answer 2

Given:

The point is (-12,-8).

Rule of transformation is $R_{270^\circ}\circ D_{\dfrac{1}{4}}$.

To find:

The coordinates of image after transformation.

Solution:

According to the rule of transformation $R_{270^\circ}\circ D_{\dfrac{1}{4}}$, first the point is dilated by factor $\dfrac{1}{4}$ with origin as center of dilation after that it was rotated 270 degrees anticlockwise.

If a point is dilated by factor $\dfrac{1}{4}$ with origin as center of dilation, then

$(x,y)\to \left(\dfrac{1}{4}x,\dfrac{1}{4}y\right)$

$(-12,-8)\to \left(\dfrac{1}{4}(-12),\dfrac{1}{4}(-8)\right)$

$(-12,-8)\to \left(-3,-2\right)$

If a point is rotated 270 degrees anticlockwise, then

$(x,y)\to (y,-x)$

$(-3,-2)\to ((-2),-(-3))$

$(-3,-2)\to (-2,3)$

Therefore, the coordinates of image after transformation are (-2,3).