Question

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

Answer 1

The image of the point (6, -2) under the same translation that moved point P(2, 3) to P'(5, -4) is (9, -9).

Step-by-step explanation:

The question is asking to find the image of a given point under the same translation that moved point P(2, 3) to point P'(5, -4). In order to find the image of a new point under the same translation, we first need to determine the translation vector used to translate point P to P'. Then, we apply this translation vector to the new point to find its image.

To find the translation vector, we subtract the coordinates of P from those of P':

• Translation vector x-coordinate = x' - x = 5 - 2 = 3
• Translation vector y-coordinate = y' - y = -4 - 3 = -7

We will apply the same translation to the new point (6, -2):

• New point's x-coordinate = 6 + 3 = 9
• New point's y-coordinate = -2 - 7 = -9

Therefore, the image of the point (6, -2) under the same translation is (9, -9).