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Question
The line segment joining the points (5, −4) and (2, 2) is divided by the points Q in the ratio 1 : 2. Does the line x – 2y = 0 contain Q?
Solution
Given, the line segment joining the points (5, −4) and (2, 2) is divided by the point Q in the ratio 1 : 2.
Co-ordinates of the point Q are
`((1 xx 2 + 2 xx 5)/(1 + 2),(1 xx 2 + 2 xx (-4))/(1 + 2))`
= `((2 + 10)/3, (2 - 8)/3)`
= `(12/3, (-6)/3)`
= (4, –2)
Substituting x = 4 and y = –2 in the given equation, we have:
L.H.S. = x − 2y
= 4 − 2(−2)
= 4 + 4
= 8 ≠ R.H.S.
Hence, the given line does not contain point Q.
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