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:
(A) $ 2x + 3y = 12 $
(B) $ 3x + 2y = 12 $
(C) $ 4x - 3y = 6 $
(D) $ 5x - 2y = 10 $

Answer 1

Hint: In order to answer this question, to find the equation of the line, we will apply the equational formula to find the equation of the line. And we will first let the coordinates of the line with the variables.

Complete step by step solution:
Let the middle point be $ P(3,2) $ .
Then the line meets the axes at $ (6,0)\,and\,(0,4) $ .
Let both the above coordinates that lie on the axes be $ A(6,0) $ and $ B(0,4) $ .
Now, we have to find the equation of the line whose coordinates are lies on the axes:
So, Equation of the line using intercept form is:-
 $ \dfrac{x}{A} + \dfrac{y}{B} = 1 $
Now, we will put the sum of the points of the coordinates at their respective point name:
 $ \Rightarrow \dfrac{x}{6} + \dfrac{y}{4} = 1 $
Now, we will do L.C.M of the denominator, to solve for the equation:-
 $ \Rightarrow 2x + 3y = 12 $
So, the required equation of the line is $ 2x + 3y = 12 $ .
Hence, the correct option is (A) $ 2x + 3y = 12 $
So, the correct answer is “Option A”.

Note: As we can see that the correct answer is an example of linear equation, The slope intercept form of a linear equation is \[y = mx + b\] , where $ m $ is the slope and $ b $ is the $ y $ intercept of the line.