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

Answer 1

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

\[3 \times \frac{- 2m + n}{m + n} + 4 \times \frac{m + 2n}{m + n} = 7\]

\[\Rightarrow - 2m + 11n = 7m + 7n\]

\[\Rightarrow - 9m = - 4n\]

\[\Rightarrow m: n = 4:9\]