Maths-
General
Easy

Question

Line 1: passes through (0, 1) and (-1, 5)
Line 2: passes through (7, 2) and (3, 1)
Line1 and line 2 are

  1. Parallel 
  2. Perpendicular
  3. Neither

The correct answer is: Perpendicular


    Hint:
    The equation of a line passing through two points (x1,y1) and (x2,y2) is
    y - y1fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction open parentheses straight x minus straight x subscript 1 close parentheses
    y = m1x + c1 and y = m2x + c2 are considered are perpendicular lines if
    m1m2 = -1
    Solution
    Equation of line passing through (0, 1) and (-1, 5) is
    y – 1 = fraction numerator 5 minus 1 over denominator negative 1 minus 0 end fraction (x – 0) 
    y – 1 = – 4x
    y = – 4x +1
    Equation of line passing through (7, 2) and (3, 1) is
    y – 2 = fraction numerator 1 minus 2 over denominator 3 minus 7 end fraction (x – 7) 
    y – 2 = 1 fourth(x–7)
    y – 2 = x over 4 – 7 over 4
    y = x over 4 + 1 fourth
    Slope of line is –4 and slope of line 2 is 1 fourth
    –4× 1 fourth = – 1
    We can see that m1 × m2 = – 1. So, line 1 and line 2 are perpendicular to each other.
    Final Answer:
    Line 1 and line 2 are perpendicular to each other. Hence, option b is correct.

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