The line segment joining the points (1, 2) and (-2, 1) is divided by t

1.	The line segment joining the points (1, 2) and (-2, 1) is divided by the line 3x + 4y = 7 in the ratio A. 3 : 4 B. 4 : 3 C. 9 : 4 D. 4 : 9
Answer» 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 \(\Big(\frac{-2m+n}{m+n},\frac{m+2n}{m+n}\Big)\) that lie on the line 3x + 4y = 7 \(3 \times \frac{-2m+n}{m+n}+4\times\frac{m+2n}{m+n}\) = 7 ⇒ - 2 + 11 n = 7 m + 7 n ⇒ - 9 m = - 4 n ⇒ m: n = 4 : 9

The line segment joining the points (1, 2) and (-2, 1) is divided by the line 3x + 4y = 7 in the ratio A. 3 : 4 B. 4 : 3 C. 9 : 4 D. 4 : 9

Answer»

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 \(\Big(\frac{-2m+n}{m+n},\frac{m+2n}{m+n}\Big)\) that lie on the line 3x + 4y = 7

\(3 \times \frac{-2m+n}{m+n}+4\times\frac{m+2n}{m+n}\) = 7

⇒ - 2 + 11 n = 7 m + 7 n

⇒ - 9 m = - 4 n

⇒ m: n = 4 : 9