Question

I is the origin and P is the (4,3). Rx and Ray are reflections around the x- and y- axes

(4,-8)
(-4,8)
(-4,-8)

Answer 1

The correct option is 1. The image of (2,4) is (4,-8).

Explanation:

The given rule is

`R_x{\circ}D_(o,2):(2,4)`

The transformations perform from right to left.
`D_(o,2)` means dilation with scale factor 2 and center of dilation is origin.

The given rule defines the dilation with scale factor 2 and center of dilation is origin followed by reflection across x-axis.

If a figure dilated by scale factor k and the center of dilation is origin, then

`(x,y)\rightarrow (kx,ky)`

The scale factor is 2,

`(x,y)\rightarrow (2x,2y)`

`(2,4)\rightarrow (4,8)`

If a figure reflected across x-axis, then x-coordinate remains the same but the sign of y-coordinate is changed.

`(x,y)\rightarrow (x,-y)`

`(4,8)\rightarrow (4,-8)`

Therefore image of (2,4) is (4,-8) and option 1 is correct.