Point P′(5, −4) is the image of point P(2, 3) under a translation. What is the image of (6, −2) under the same translation? A. (7, −1) B. (13, −3) C. (9, −9) D. (3, 5)

Question

asked Aug 9, 2021 50.6k views

2 Answers

Blackpen · Answer 1 · 2021-08-13T18:10:21+0000

Answer:

C. (9, -9)

Explanation:

From Linear Algebra, we understand translations as the following vector sum:

P'(x,y) = P(x,y) +U(x, y) (Eq. 1)

Where:

P(x,y) - Original vector with respect to origin, dimensionless.

U(x,y) - Translation vector, dimensionless.

P'(x,y) - Translated vector with respect to origin, dimensionless.

If we know that
P(x,y) = (2,3) and
P'(x,y) =(5,-4) , then the translation vector is:

U(x,y) = P'(x,y)-P(x,y)

U(x,y) = (5,-4)-(2,3)

U(x,y) =(5-2,-4-3)

U(x,y) =(3,-7)

Now, if we assume that
P(x,y) = (6,-2) , then the translated vector is:

P'(x,y) =(6,-2) +(3,-7)

P'(x,y) =(9,-9)

Hence, the correct answer is C.