BECE Mathematics 2010 Paper

Concept:Translation vector = Image point − Original point. In coordinate form, subtract corresponding coordinates.Explanation:The original point is $P = (4,5) = \binom{4}{5}$.The image point after translation is $P' = (3,1) = \binom{3}{1}$.Let the translation vector be $v$.We know $P + v = P'$.Therefore, $v = P' - P$.So, $v = \binom{3}{1} - \binom{4}{5}$.Subtract the $x$-coordinates and the $y$-coordinates separately:$v = \binom{3 - 4}{1 - 5}$.$v = \binom{-1}{-4}$.Answer:The translation vector is $\binom{-1}{-4}$, so the correct option is D.