1.

The equation of the line parallel to the line 2x - 3y = 7 and passing through the middle point of the line segment joining the points (1, 3) and (1, -7) is:1. 2x - 3y - 4 = 02. 2x - 3y + 4 = 03. 2x - 3y - 8 = 04. 2x - 3y + 8 = 0

Answer» Correct Answer - Option 3 : 2x - 3y - 8 = 0

Concept:

  • The co-ordinates of a point P, dividing the line joining the points A(x1, y1) and B(x2, y2) in the ratio m : n internally, are given by:

    \(\rm P\left(\dfrac{nx_1+mx_2}{m+n},\dfrac{ny_1+my_2}{m+n} \right)\)

  • The equation of a line parallel to the line ax + by + c = 0 is k(ax + by) + c = 0, where k is any non-zero number.

 

Calculation:

The mid-point divides a line in the ratio 1 : 1 internally.

∴ The co-ordinates of the midpoint (M) of points (1, 3) and (1, -7) will be: \(\rm M\left(\dfrac{1\times1+1\times1}{1+1},\dfrac{1\times3+1\times(-7)}{1+1} \right)\) = M (1, -2).

The equation of the line parallel to the line 2x - 3y - 7 = 0 can be assumed to be k(2x - 3y) - 7 = 0.

Since this line passes through M(1, -2), we will get:

k[2(1) - 3(-2)] - 7 = 0

⇒ k(2 + 6) - 7 = 0

⇒ k = \(\dfrac78\).

The equation, therefore, is:

k(2x - 3y) - 7 = 0

⇒ \(\rm\dfrac78(2x-3y)-7=0\)

⇒ 2x - 3y - 8 = 0.


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