Question

The point $C(–1,2)$ divides the lines segment $AB$ in the ratio 3:4, where the coordinates of $A$ are $(2,5)$. The coordinates of $B$ is:

• A. (–5, –2)
• B. (–1, – 2)
• C. (–4, – 2)
• D. (5, – 4)

Answer 1

The correct option is A

(–5, –2)

Let $C(-1,2)$ divides the line joining $A(2,5)$ and $B(x,y)$ in the ratio 3:4. Then:

$C(\frac{3x+8}{7},\frac{3y+20}{7})=C(-1,2)$

$\Rightarrow \frac{3x+8}{7}=-1$ & $\frac{3y+20}{7}=2$

$\Rightarrow 3x+8=-7$ & $3y+20=14$

$\Rightarrow$ $x=-5$ & $y=-2$

The coordinates of $B$ are: $B(-5,-2)$