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___________.

(–5, –2)

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(–1, – 2)

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(–4, – 2)

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(5, – 4)

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Solution

The correct option is A
(–5, –2)

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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Similar questions

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

C = (\frac{12}{5}, \frac{- 1}{5}, \frac{4}{5})

A B

3 : 2

B = (2, - 1, 2)

A

(a) Write down the coordinates of the point P that divides the line joining A (-4, 1) and B (17, 10) in the ratio 1:2.

(b) Calculate the distance OP were O is the origin.

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