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What is the equation of the straight line which passes through the point of intersection of the straight lines x + 2y = 5 and 3x + 7y = 17 and is perpendicular to the straight line 3x + 4y = 10?

What is the equation of the straight line which passes through the point of intersection of the straight lines x + 2y = 5 and 3x + 7y = 17 and is perpendicular to the straight line 3x + 4y = 10? Correct Answer 4x – 3y + 2 = 0

Concept:

  • When two lines are perpendicular, the product of their slope is -1. If m is the slope of a line, then the slope of a line perpendicular to it is -1/m.
  • Equation of line is (y – y1) = m(x – x1)

 

Calculation:

x + 2y = 5                                 …. (1)

3x + 7y = 17                             …. (2)  

Solving equation 1 and 2, we get

x = 1 and y = 2

Point of intersection: (x, y) = (x1, y1) = (1, 2)

Let slope of the straight line 3x + 4y = 10 is m1,

∴ Slope (m1) = -3/4

We know that when two lines are perpendicular, the product of their slope is -1.

Slope of perpendicular line = -1/m1 = 4/3 = m

Equation of line: (y – y1) = m(x – x1)

⇒ y – 2 = 4/3 (x – 1)

⇒ 3y – 6 = 4x – 4

∴ 4x – 3y + 2 = 0

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