Question

If the coordinates of the middle point of the portion of a line intercepted between the coordinate axes is (3, 2), then the equation of the line will be ______.

Options

• 2x + 3y = 12

• 3x + 2y = 12

• 4x – 3y = 6

• 5x – 2y = 10

Answer 1

If the coordinates of the middle point of the portion of a line intercepted between the coordinate axes is (3, 2), then the equation of the line will be 2x + 3y = 12.

Explanation:

Let the given line meets the axes at A(a, 0) and B(0, b).

Given that C(3, 2) is the mid-point of AB

∴ 3 = (a + 0)/2`

⇒ a = 6

And 2 = `(0 + b)/2`

⇒ b = 4

Intercept form of the line AB

`x/a + y/b` = 1

⇒ `x/6 + y/4` = 1

⇒ 2x + 3y = 12