Question

Triangle PQR has vertices P(−3,4), Q(−8,3), and R(−1,−6). Triangle PQR is dilated by a scale factor of 8 centered at the origin to get triangle P′Q′R′.

What are the coordinates of points P′, Q′, and R′ of the image?

P′(−38,−12), Q′(−1,38), R′(−18,−34)
P′(−3,32), Q′(−8,24), R′(−1,−48)
P′(−24,4), Q′(−64,3), R′(−8,−6)
P′(−24,32), Q′(−64,24), R′(−8,−48)

Answer 1

(-24, 32), (-64, 24) and (-8,-48)

Explanation:

Answer 2

The coordinates of points P', Q' and R' are (-24, 32), (-64, 24) and (-8,-48), respectively.

Explanation:

Vectorially speaking, the dilation of a vector with respect to a given point is defined by the following formula:

`P'(x,y) = O(x,y) + r\cdot [P(x,y)-O(x,y)]`,
`r > 1` (1)

Where:

`O(x,y)` - Point of reference.

`P(x,y)` - Original point.

`P'(x,y)` - Dilated point.

`r` - Scale factor.

If we know that
`O(x,y) = (0,0)`,
`P(x,y) = (-3, 4)`,
`Q(x,y) = (-8,3)`,
`R(x,y) = (-1,-6)` and
`r = 8`, then the new coordinates of the triangle are, respectively:

`P'(x,y) = (0,0) + 8\cdot [(-3,4)-(0,0)]`

`P'(x,y) = (-24, 32)`

`Q'(x,y) = (0,0) + 8\cdot [(-8,3)-(0,0)]`

`Q'(x,y) = (-64, 24)`

`R'(x,y) = (0,0) + 8\cdot [(-1,-6)-(0,0)]`

`R'(x,y) = (-8,-48)`

The coordinates of points P', Q' and R' are (-24, 32), (-64, 24) and (-8,-48), respectively.