Question

Point P′(5, −4) is the image of point P(2, 3) under a translation. Select is the image of (6, −2) under the same translation?

A. (7, −1)
B. (13, −3)
C. (9, −9)
D. (3, 5)

Answer 1

The image of (6, −2) under the same translation that moved P to P' is found by applying the same translation vector. After doing so, we determine that the coordinates (9, −9) represent the correct image, corresponding to option C.

Step-by-step explanation:

To find the image of (6, −2) under the same translation that moved point P(2, 3) to P′(5, −4), we need to apply the same change in position (also known as the translation vector) to (6, −2). Let's determine the translation vector first. To get from P to P′, the x-coordinate increases by 3 (from 2 to 5) and the y-coordinate decreases by 7 (from 3 to −4). Therefore, the translation vector is (3, -7).

Applying this translation vector to (6, −2), we add 3 to the x-coordinate (6 + 3 = 9) and subtract 7 from the y-coordinate (−2 − 7 = −9). Thus, the translated point is (9, −9), which corresponds to option C.