Question

After applying the composition R0.90 ry to RS what are the coordinates of R1 and S1?

Answer 1

B. R(-1, 3), S'(-5,3)
A 90-degree rotation about the origin has the rule of (x,y) changes to (y, -x).

Answer 2

The coordinates of image are R'(1,3) and S'(5,3).

Explanation:

From the given figure it is clear that the coordinates of the points R and S are R(-3,-1) and S(-3,-5).

The composition
`R_(0,90^(\circ))\circ r_y` means the figure reflected across y-axis and then rotate 90 degree counterclockwise about the origin.

If a figure reflected across y-axis then

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

`R(-3,-1)\rightarrow R_1(3,-1)`

`S(-3,-5)\rightarrow S_1(3,-5)`

If a figure rotate 90 degree counterclockwise about the origin, then

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

`R_1(3,-1)\rightarrow R'(1,3)`

`S_1(3,-5)\rightarrow S'(5,3)`

Therefore the coordinates of image are R'(1,3) and S'(5,3).