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:

The line segment joining the CBSE 10th Board

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  divides the line joining the points  and  in the ratio , then coordinates of point

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

Here, it is given that  and 
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)

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