Question

The composition D (idk) is applied to RST to create the image of R”S”T”, which is not shown,

what are the coordinates of point S”

Answer 1

The correct answer is the first choice: (-3/2 , 9/2),

To find the new points, you have to perform both of the transformations listed. First is a dilation by 3/2. Then, a second dilation must be performed by 1/2.

This means you multiply the values by 3/2, then 1/2.

The points changes from (-2, 6) to (-3, 9) to (-3/2, 9/2).

Answer 2

The correct option is 1.

Explanation:

From the given figure it is clear that the vertices of triangle RST are

R(-6,10), T(-10,0) and S(-2,6).

The given composition is
`D_{0,(3)/(2)}(x,y)\circ D_{0,(1)/(2)}(x,y)`, it means the figure dilated by factor 1/2 with center of dilation is origin, then the figure dilated by factor 3/2 with center of dilation is origin.

If a point dilated by factor k with center of dilation is origin, then

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

The coordinates of S after dilation by factor 1/2 with center of dilation is origin is

`S(-2,6)\rightarrow S'((1)/(2)(-2),(1)/(2)(6))=S'(-1,3)`

The coordinates of S' after dilation by factor 3/2 with center of dilation is origin is

`S'(-1,3)\rightarrow S''((3)/(2)(-1),(3)/(2)(3))= S''(-(3)/(2),(9)/(2))`

The coordinates of S'' are
`S''(-(3)/(2),(9)/(2))`

Therefore the correct option is 1.