Q17 of 112 Page 163

A straight line cuts the coordinate axes at A and B. If the midpoint of AB is (3, 2), then

find the equation of AB.

The mid–point of AB is in the 1st quadrant as both the intercepts are positive.


Thus A will lie on the y –axis and B will lie on the x axis


Let A be ( 0,a) and B be (b,0)


By the mid–point theorem, the coordinates of mid–point are


( = (3,2)


⇒


⇒ and


⇒ B = 6 and a = 4


Thus y intercept is 4 and x intercept is 6


The equation of the line using the intercept form is



⇒


⇒ 4x + 6y = 24


⇒ 2x + 3y –12 = 0


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