Question

The point which divides the line segment joining the points A(7, −6) and B(3, 4) in the ratio 1 : 2 lies in

(a) I quadrant
(b) II quadrant
(c) III quadrant
(d) IV quadrant

Answer 1

(d) IV quadrant
The given points are $A\left(7,-6\right)$and $B\left(3,4\right)$.
Then, $\left(x_1=7,y_1=-6\right)\text{and}\left(x_2=3,y_2=4\right)$
Also, m = 1 and n = 2
Let the required point be $P\left(x,y\right)$.
By section formula, we have
$x=\frac{\left(1\times 3+2\times 7\right)}{\left(1+2\right)},y=\frac{\left(1\times 4+2\times \left(-6\right)\right)}{\left(1+2\right)}$
$\Rightarrow x=\frac{17}{3},y=\frac{-8}{3}$
Hence, the coordinates of P are$\left(\frac{17}{3},\frac{-8}{3}\right)$, which lies in the IV quadrant.