Question

The co-ordinates of the point which divides (internally) the line joining the points (– 2, – 2) and (– 5, 7) in the ratio 2 : 1 are

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

Answer 1

The correct option is C

(– 4, 4)

Let the required point be (a, b).

Here, point (a, b) divides the line joining the points (– 2, – 2) and (– 5, 7) in the ratio 2 : 1.

We know that co-ordinates of the point that divides (internally) the line joining the points $(x_1,y_1)$ and $(x_2,y_2)$ in the ratio m : n are

(x, y) = $(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})$

$\Rightarrow a$ = $\frac{2(-5)+1(-2)}{2+1}$ = -4

$b$ = $\frac{2\left(7\right)+1(-2)}{2+1}$ = 4

Therefore, co-ordinates of the point are (-4, 4).