Question

The line 3x + y – 9 = 0 divides the line joining the points (1, 3) and (2, 7) internally in the ratio ______.

विकल्प

• 3 : 4

• 3 : 2

• 2 : 3

• 4 : 3

Answer 1

The line 3x + y – 9 = 0 divides the line joining the points (1, 3) and (2, 7) internally in the ratio 3 : 4.

Explanation:

Let the line 3x + y – 9 = 0 divide the line segment joining A(l, 3) ad B(2, 7) in the ratio K : 1 at point C.

The coordinates of C are `((2"K" + 1)/("K + 1")) + ("7K" + 3)/("K + 1")`

But the point C lies on the line 3x + y - 9 = 0

`therefore 3((2"K" + 1)/("K + 1")) + ("7K" + 3)/("K + 1") - 9 = 0`

⇒ 6K + 3 + 7K + 3 - 9 - 9K = 0

⇒ 4K - 3 = 0

⇒ K = `3/4`

∴ Required ratio = 3 : 4