Question

Graph APQR with vertices P(4,8), Q(-4, 0), and R(8,0) and its image after a dilation with scale factor 0.75 centered at the origin. State the coordinates of P', Q' and R'.

a) P'(3, 6), Q'(-3, 0), R'(6, 0)
b) P'(6, 12), Q'(-6, 0), R'(12, 0)
c) P'(2, 4), Q'(-2, 0), R'(4, 0)
d) P'(5, 10), Q'(-5, 0), R'(10, 0)

Answer 1

After performing a dilation with a scale factor of 0.75 centered at the origin on triangle APQR, the new coordinates of the image are P'(3, 6), Q'(-3, 0), and R'(6, 0), which is option (a).

Step-by-step explanation:

To graph triangle APQR with vertices P(4,8), Q(-4, 0), and R(8,0) and its image after a dilation with a scale factor of 0.75 centered at the origin, we need to multiply each coordinate of the vertices by 0.75. This will give us the new coordinates of the image, P', Q', and R'.

For point P, the calculations will be:
P'(0.75×4, 0.75×8) = P'(3,6).

For point Q, the calculations will be:
Q'(0.75×-4, 0.75×0) = Q'(-3,0).

For point R, the calculations will be:
R'(0.75×8, 0.75×0) = R'(6,0).

Therefore, the correct coordinates after the dilation are P'(3, 6), Q'(-3, 0), and R'(6, 0), which corresponds to option (a).