Question

The point P divides the join of (2, 1) and (−3, 6) in the ratio 2 : 3. Does P lies on the line x − 5y + 15 = 0?

Answer 1

Given, the point P divides the join of (2, 1) and (−3, 6) in the ratio 2 : 3.

Co-ordinates of the point P are

`((2 xx (-3) + 3 xx 2)/(2 + 3),(2 xx 6 + 3 xx 1)/(2 + 3))`

= `((-6 + 6)/(5), (12 + 3)/(5))`

= `(0/5, 15/5)`

= (0, 3)

Substituting x = 0 and y = 3 in the given equation, we have:

L.H.S. = 0 − 5(3) + 15

= −15 + 15

= 0 = R.H.S.

Hence, the point P lies on the line x − 5y + 15 = 0.