If the point C (–1, 2) divides internally the line segment joining A (2, 5) and B in ratio 3 : 4, find the coordinates of B.

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Solution

Let the coordinates of B be $(α, β)$ . It is given that AC:BC = 3:4. So, the coordinates of C are

$\frac{3 α + 4 \times 2}{3 + 4}, \frac{3 β + 4 \times 5}{3 + 4}$ = $\frac{3 α + 8}{7}, \frac{3 β + 20}{7}$

but, the coordinates of C are (-1, 2)

$\frac{3 α + 8}{7}$ = -1 and $\frac{3 β + 20}{7}$ = 2

$\Rightarrow α$ = -5 and $β$ = -2

Thus, the coordinates of B are (-5, -2).

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If the point C (–1,2) divides the lines segment AB in the ratio 3 : 4, where the co-ordinates of A is (2, 5), then coordinates of B is

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