Question

The point P (5, – 4) divides the line segment AB, as shown in the figure, in the ratio 2 : 5. Find the co-ordinates of points A and B. Given AP is smaller than BP.

Answer 1

From the figure, the line AB intersects x-axis at A and y-axis at B.

Let the co-ordinates of A (x, 0) and B (0, y) and P (5, –4) divides it in the ratio of 2 : 5

∴ `5 = (2 xx 0 + 5 xx x)/(2 + 5)`

`5 = (0 + 5x)/7`

∴ 5x = 35

`x = 35/5`

x = 7

Again, `-4 = (2 xx y + 5 xx 0)/(2 + 5)`

`-4 = (2y + 0)/7`

∴ 2y = –4 × 7 = –28

`y = (-28)/2`

y = –14

∴ Co-ordinates of A are (7, 0) and of B are (0, –14)