Q10 of 37 Page 1

If is the mid-point of the line segment joining the points (2, 0) and , then show that the line 5x + 3y + 2 = 0 passes through the point (–1, 3p).

We have


Let points be A(2, 0), B(0, ) and C(1, ).


Given that, C(1, ) is the midpoint, it can be expressed as


(1, ) =


⇒ (1, ) =


⇒ (1, ) = (1, )


By comparing, we get



⇒ p =


To show that the line 5x + 3y + 2 = 0 passes through the point (-1, 3p), we need to find the point (-1, 3p).


Since, p = 1/3


⇒ (-1, 3p) = (-1, 3 × 1/3) = (-1, 1)


Now compare (x, y) from (-1, 1), we get


x = -1 and y = 1


Putting these values in 5x + 3y + 2 = 0,


We get 5(-1) + 3(1) + 2 = 0


⇒ -5 + 3 + 2 = 0


⇒ -5 + 5 = 0


⇒ 0 = 0


⇒ LHS = RHS


Hence, verified that the line 5x + 3y + 2 = 0 passes through the point (-1, 1).


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