Question

The point P which divides the line segment joining the points

$A(2,-5)$, and $B(5,2)$ in the ratio $2:3$ lies in the quadrant
(a) I

(b) II

(c) III

(d) IV

Answer 1

Let $(x,y)$ be the coordinates of $P$.

Point $P$ divides the line joining $A(2,-5)$ and $B(5,2)$

in the ratio $2:3$

Here, $x_1=2,y_1=-5,x_2=5,y_2=2$ and $m=2,n=3$

By section formula,we have

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

$x=\frac{(2\times 5)+(3\times 2)}{2+3}=\frac{10+6}{5}$

$=\frac{16}{5}$

$y=\frac{(2\times 2)+(3\times -5)}{2+3}$

$=\frac{4-15}{5}$

$=\frac{-11}{5}$

Thus, the coordinates of point $P$ are $\frac{16}{5},\frac{-11}{5}$ and so it lies in the fourth quadrant.
Hence, the correct answer is option (d).