Question

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)

Answer 1

Answer:

C. (9, -9)

Step-by-step 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.

Answer 2

Answer: (9, −9)c

Step-by-step explanation: