Find the vector which translates the point (4,-5) to (3,-2)

Correct Answer is : (−13) {-1}{3}(3−1)

Correct Answer is : (−13) {-1}{3}(3−1)

Test Index

BECE Mathematics 2013 Paper

Question : 18

Total: 40

(4,-5)

(3,-2)

Solution:

Concept:

A translation moves a point by adding a vector:

\text{Point} + \text{Vector} = \text{Image}

Explanation:

Let the translation vector be

\binom{x}{y}

The starting point is

\binom{4}{-5}

and the image is

\binom{3}{-2}

So,

\binom{4}{-5} + \binom{x}{y} = \binom{3}{-2}

Add the vectors component-wise:

\binom{4+x}{-5+y} = \binom{3}{-2}

Equate the top components:

4 + x = 3

x = 3 - 4 = -1

Equate the bottom components:

-5 + y = -2

y = -2 + 5 = 3

Therefore, the translation vector is

\binom{-1}{3}

Answer:

\binom{-1}{3}

(Option B).

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