The co-ordinates of the points which divides the line joining (– 2, – 2) and (– 5, 7) in the ratio 2 : 1 is _____.

(4, – 4)

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(– 3, 1)

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(– 4, 4)

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(1, – 3)

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Solution

The correct option is C
(– 4, 4)

If a point P(x,y) divides the line joining $(x_{1}, y_{1}) and (x_{2}, y_{2})$ in the ratio m:n
then $x$ = $\frac{m x_{2} + n x_{1}}{m + n}$ and y = $\frac{m y_{2} + n y_{1}}{m + n}$

$∴ x$ = $\frac{m x_{2} + n x_{1}}{m + n}$ = $\frac{2 (- 5) + 1 (- 2)}{2 + 1}$ = -4

and $y$ = $\frac{m y_{2} + n y_{1}}{m + n}$ = $\frac{2 (7) + 1 (- 2)}{2 + 1}$ = 4

$∴$ the required point is (-4,4).

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The co-ordinates of the points which divides the line joining (– 2, – 2) and (– 5, 7) in the ratio 2 : 1 is _____.

The correct option is C (– 4, 4) If a point P(x,y) divides the line joining (x1,y1) and (x2,y2) in the ratio m:n then x = mx2+nx1m+n and y = my2+ny1m+n ∴x = mx2+nx1m+n = 2(−5)+1(−2)2+1 = -4 and y = my2+ny1m+n = 2(7)+1(−2)2+1 = 4 ∴ the required point is (-4,4).