Question

A point P divides the straight line joining X(1, -2) and Y(5,3) internally in a ratio 2:3. Find the coordinates of P.

a) (2,0)
b) (3,1)
c) (3,0)
d) (2,1)

Answer 1

The coordinates of point P are (13/5, 0).

Step-by-step explanation:

To find the coordinates of point P, we can use the concept of section formula. The section formula states that if a point P divides the line joining points A and B internally in the ratio m:n, then its coordinates can be found using the formulas:

x-coordinate of P = (mx2 + nx1)/(m + n)

y-coordinate of P = (my2 + ny1)/(m + n)

In this case, the coordinates of point X are (1, -2) and the coordinates of point Y are (5, 3). The ratio in which point P divides the line is 2:3. Plugging these values into the formulas, we get:

x-coordinate of P = (2*5 + 3*1)/(2 + 3) = 13/5

y-coordinate of P = (2*3 + 3*(-2))/(2 + 3) = 0

Therefore, the coordinates of point P are (13/5, 0).