BECE Mathematics 2021 Paper

Concept:A translation moves every point by the same vector. If $P$ is moved by $r = \binom{a}{b}$ to $P'$, then $P' = P + r$, so the vector is $r = P' - P$ (image minus original).Given:Original point $P(10, -3)$, image $P'(4, 5)$Solution:Subtract the coordinates of $P$ from those of $P'$:$x$-component: $4 - 10 = -6$$y$-component: $5 - (-3) = 5 + 3 = 8$$$r = \binom{-6}{8}$$Check: $P + r = (10 + (-6),\; -3 + 8) = (4, 5) = P'$ ✓Key point: Subtracting the other way ($P - P'$) gives $\binom{6}{-8}$ (option B), which is the vector that moves $P'$ back to $P$.Answer:Option C ($\binom{-6}{8}$)