The line segment joining the points A(4,-5) and B(4,5) is divided by

Q) The line segment joining the points A(4,-5) and B(4,5) is divided by the point P such that AP : AB = 2 : 5. Find the coordinates of P.

Ans: Let’s draw the diagram to solve:

Given that $\frac{AP}{AB} = \frac{2}{5}$

$\therefore \frac{AP}{AP+PB} = \frac{2}{5}$ (AB = AP + PB)

by cross multiplication, we get: 5 AP = 2 (AP + PB)

or $\frac{AP}{PB} = \frac{2}{3}$

By section formula, if a point $(x, y)$ divides the line joining the points $(x 1, y 1)$ and $(x 2, y 2)$ in the ratio $m : n$ , then coordinates of point $(x, y) =$

( $\frac{mx_1+nx_2}{m+n}$ , $\frac{my_1+ny_2}{m+n}$ )

Here, it is given that

A (4, -5) = (x 1, y 1)

and

B (4, 5) = (x 2, y 2), m : n = 2 : 3

Hence the co-ordinates of point P:

$\therefore$ x = $\frac{(2 \times 4 + 3 \times 4)}{(2+3)}$ = 4

Similarly, y = $\frac{(2 \times 5 + 3 \times -5)}{(2+3)}$ = -1

Therefore, the coordinates of P are (4, -1)

Leave a Comment Cancel Reply

Contact us

Join us

Useful Link

Our Quizzes

Related Posts

Leave a Comment Cancel Reply