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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)

User DeeveeABC
by
8.3k points

2 Answers

4 votes

Answer: (9, −9)c

Explanation:

User Chklang
by
7.4k points
4 votes

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.

User Blackpen
by
8.3k points
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