Question

A line segment PQ has endpoints P at (12,-4) and Q at (-16,8). As a result of dilation about the origin, the endpoint of P' has coordinates (18,-6). What are the coordinates of Q'?

A. (-24,12)
B. (-22,10)
C. (-11,5)
D. (-10,6)

Answer 1

To find the coordinates of Q' after dilation about the origin, we can use the formula (x', y') = (k * x, k * y), where (x, y) are the original coordinates of a point, (x', y') are the new coordinates after dilation, and k is the scale factor of the dilation. By substituting the known coordinates of P and P' into the formula and solving for the scale factor, we find that k = 1.5. Finally, we use the scale factor to find the coordinates of Q' as (-24, 12).

Step-by-step explanation:

To find the coordinates of Q' after dilation about the origin, we can use the formula:

(x', y') = (k * x, k * y)

where (x, y) are the original coordinates of a point, (x', y') are the new coordinates after dilation, and k is the scale factor of the dilation.

Since we know the coordinates of P (12, -4) and P' (18, -6), we can substitute these values into the formula to find the scale factor:

18 = k * 12

-6 = k * -4

Solving these equations, we find that k = 1.5.

Now we can use the scale factor to find the coordinates of Q'.

Q' = (k * x, k * y)

= (1.5 * -16, 1.5 * 8)

= (-24, 12)

Therefore, the coordinates of Q' are (-24, 12).