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

Answer:

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

Step-by-step 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.