If P(3, 4) is the mid-point of a line segment between the axes, then what is the equation of the line?

Concept:

• Midpoint of (x1,y1) and (x2,y2) =  \(\left({x_1+ x_2 \over 2} , {y_1 + y_2 \over 2} \right)\)

• The equation of the line passing through (x₁,y₁) and (x₂,y₂) is

  \((y - y_1) = {y_2- y_1 \over x_2 - x_1} (x - x_1)\)

Calculation:

Let the points of line on axes be (h,0) and (0,k) respectively

So, P(3, 4) is the mid-point of (h,0) and (0,k)

⇒ (3,4) = \(\left({h+ 0 \over 2} , {0+k \over 2} \right)\)

⇒ h = 6 and k = 8

So, the line passes through the points (6,0) and (0,8)

⇒ The equation of the line passing through (6,0) and (0,8) is

\((y - 0) = {8- 0 \over 0 -6} (x - 6)\)

⇒ -6y = 8x - 48

⇒ 4x + 3y − 24 = 0

∴ The correct option is (2).