Question

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

• A. (1, – 3)
• B. (– 3, 1)
• C. (– 4, 4)
• D. (4, – 4)

Answer 1

The correct option is C

(– 4, 4)

If a point P(x,y) divides the line joining $(x_1,y_1)\text{and}(x_2,y_2)$ in the ratio m:n
then $x$ = $\frac{m{x}_2+n{x}_1}{m+n}$ and y = $\frac{m{y}_2+n{y}_1}{m+n}$

$\therefore x$ = $\frac{m{x}_2+n{x}_1}{m+n}$ = $\frac{2(-5)+1(-2)}{2+1}$ = -4

and $y$ = $\frac{m{y}_2+n{y}_1}{m+n}$ = $\frac{2\left(7\right)+1(-2)}{2+1}$ = 4

$\therefore$ the required point is (-4,4).