The point C (–1,2) divides the line segment AB in the ratio 3:4, w

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Question

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

Options:

A . (–5, –2)

B . (–1, – 2)

C . (–4, – 2)

D . (5, – 4)

Answer: Option A
:
A

If a point $P (x, y)$ divides a line segment joining $(x_{1}, y_{1}) and (x_{2}, y_{2})$ in the ratio $m : n$ , then the coordinates of P are given by:
$x = \frac{m x_{2} + n x_{1}}{m + n}, y = \frac{m y_{2} + n y_{1}}{m + n}$
Let $C (- 1, 2)$ divide the line joining $A (2, 5)$ and $B (x, y)$ in the ratio 3:4.
Then,
$C (\frac{3 x + 8}{7}, \frac{3 y + 20}{7})$ = C(-1, 2)
$\Rightarrow \frac{3 x + 8}{7} = - 1 3 x + 8 = - 7 \Rightarrow x = - 5 \Rightarrow \frac{3 y + 20}{7} = 2 3 y + 20 = 14 \Rightarrow y = - 2$
Thus, the coordinates of B are $B (- 5, - 2) .$

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