Question

If d 3/4 (PQR)=(P’Q’R), what are the coordinates of r?

A. (4/3,-4)
B. (3/4,-9/4)
C. (3,4)
D. (-9/4,0)
Please help! I just don’t understand how to do this.

Answer 1

Answer: The correct option is B.

Step-by-step explanation:

From the figure it is noticed that the coordinates of option point R is (1,-3).

The statement,

`d_{(3)/(4)(PQR)=P'Q'R'`

Means dilation of triangle PQR with scale factor
`(3)/(4)` and center at origin, then the image is P'Q'R'.

If the dilation with factor k and center at origin, then

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

Since the coordinates of R is (1,-3) and the scale factor is
`(3)/(4)`.

`R(x,y)\rightarrow R'((3)/(4)x,(3)/(4)y )`

`R(1,-3)\rightarrow R'((3)/(4)*1, (3)/(4)*(-3))`

`R(1,-3)\rightarrow R'((3)/(4), (-9)/(4))`

Therefore the correct option is B.