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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?
Solution
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.
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