Question

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

Answer 1

Answer: -2,3

Explanation:

Answer 2

Given:

The point is (-12,-8).

Rule of transformation is
`R_(270^\circ)\circ D_{(1)/(4)}`.

To find:

The coordinates of image after transformation.

Solution:

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

If a point is dilated by factor
`(1)/(4)` with origin as center of dilation, then

`(x,y)\to \left((1)/(4)x,(1)/(4)y\right)`

`(-12,-8)\to \left((1)/(4)(-12),(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).