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Question
The line segment joining the points (1, 2) and (−2, 1) is divided by the line 3x + 4y = 7 in the ratio ______.
Options
3:4
4:3
9:4
4:9
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Solution
The line segment joining the points (1, 2) and (−2, 1) is divided by the line 3x + 4y = 7 in the ratio 4:9.
Explanation:
Let the line segment joining the points (1, 2) and (−2, 1) be divided by the line 3x + 4y = 7 in the ratio m:n.
Then, the coordinates of this point will be \[\left( \frac{- 2m + n}{m + n}, \frac{m + 2n}{m + n} \right)\] that lie on the line.
3x + 4y = 7
\[3 \times \frac{- 2m + n}{m + n} + 4 \times \frac{m + 2n}{m + n} = 7\]
\[\Rightarrow - 2m + 11n = 7m + 7n\]
\[\Rightarrow - 9m = - 4n\]
\[\Rightarrow m: n = 4:9\]
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