The point P which divides the line segment joining the points A(2, −5) and B(5, 2) in the ratio 2 : 3
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
Solution:
Let (x, y) be the coordinates of P. Then
$x=\frac{2 \times 5+3 \times 2}{2+3}=\frac{10+6}{5}=\frac{16}{5}$
$y=\frac{2 \times 2+3 \times(-5)}{2+3}=\frac{4-15}{5}=\frac{-11}{5}$
Thus, the coordinates of point $P$ are $\left(\frac{16}{5}, \frac{-11}{5}\right)$ and so it lies in the fourth quadrant.
Hence, the correct answer is option (d).