The vertices of triangle PQR are located at P(0,1), Q(2, 2) and R(1, -3). After PQR has been dilated with scale factor 4 centered at the origin, what are the coordinates (x, y) of the image point R' ?

Question

x-coordinate of R' = Answer

y-coordinate of R' =

Answer 1

To find the coordinates of the image point R' after dilating triangle PQR with a scale factor of 4 centered at the origin, we apply the dilation transformation to the coordinates of point R.

The coordinates of point R are given as R(1, -3).

The formula for dilation centered at the origin with a scale factor \( k \) is:

\[ (x', y') = (kx, ky) \]

For R (1, -3) and a scale factor of 4, we have:

• \( x' = 4 \times 1 = 4 \)
• \( y' = 4 \times (-3) = -12 \)

Therefore, the coordinates of the image point R' after dilation are:

\[ R'(4, -12) \]

Thus, the answers are:

x-coordinate of R' = 4

y-coordinate of R' = -12