# 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 (xy) 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).

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