Mathematics
Grade9
Easy

Question

Identify the pair of parallel lines.

  1. PR and EF
  2. XY and AB
  3. EF and XY
  4. AB and PR

hintHint:

In this question, we have to find the parallel pair of lines. if the co-ordinates of line AB are A(-2,2) and B(3,2), EF are E(5,1) and F(3,-4), PR are P(-1,3) and R(-3,-2) and XY are X(-1,2) and Y(1,-3). Firstly we will calculate the slope of the lines. Later, we will the lines with same slope, as the lines with same slope will be the parallel lines.

The correct answer is: PR and EF


    The co-ordinates of line AB are A(-2,2) and B(3,2), EF are E(5,1) and F(3,-4), PR are P(-1,3) and R(-3,-2) and XY are X(-1,2) and Y(1,-3).
    Slope of line AB
    equals fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction
equals fraction numerator 2 minus 2 over denominator 3 minus left parenthesis negative 2 right parenthesis end fraction
equals 0 over 5
equals 0
    Slope of line EF
    equals fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction
equals fraction numerator negative 4 minus 1 over denominator 3 minus 5 end fraction
equals fraction numerator negative 5 over denominator negative 2 end fraction
equals 5 over 2
    Slope of line PR
    equals fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction
equals fraction numerator negative 2 minus 3 over denominator negative 3 minus left parenthesis negative 1 right parenthesis end fraction
equals fraction numerator negative 5 over denominator negative 2 end fraction
equals 5 over 2
    Slope of line XY
    equals fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction
equals fraction numerator negative 3 minus 2 over denominator 1 minus left parenthesis negative 1 right parenthesis end fraction
equals fraction numerator negative 5 over denominator 2 end fraction
    As the slope of EF =Slope of PR
    So, EF and PR are parallel lines.

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