Question

Point F(6, 1) is dilated by a scale factor of 3. The center of dilation is R(4, 1). What are the coordinates of F’ ?

(A) (6, 1)
(B) (12, 3)
(C) (10, 1)
(D) (18, 3)

Answer 1

After dilating Point F(6, 1) by a scale factor of 3 with the center of dilation at R(4, 1), the new coordinates of the point F' are (10, 1).

Step-by-step explanation:

When Point F(6, 1) is dilated by a scale factor of 3 with the center of dilation at R(4, 1), we shift Point F away from R proportionally to the scale factor. The horizontal distance from R to F is 2 units (from 4 to 6 on the x-coordinate), and since the dilation scale factor is 3, we multiply this distance by 3, giving us 6 units. Adding these 6 units to the original x-coordinate of R gives us an x-coordinate of 10 for F'. Since the y-coordinate is the same for R and F, it remains 1 for F'. Therefore, the coordinates of F' are (10, 1).