Mathematics
Grade9
Easy

Question

The points (-5,-3), (1,1),(4,3) are _______________.

  1. Collinear
  2. Non-Collinear
  3. Coplanar
  4. Both a and b

hintHint:

To find relation of the three lines we need to find slope with the formula fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction. Now if all three would be same than they would be collinear.

The correct answer is: Collinear


    A(-5,-3), B(1,1) C(4,3)
    Slope of line AB=fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction                Slope of line BC=fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction        Slope of line AC =fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction
    equals fraction numerator 1 minus left parenthesis negative 3 right parenthesis over denominator 1 minus left parenthesis negative 5 right parenthesis end fraction
equals fraction numerator 1 plus 3 over denominator 1 plus 5 end fraction
equals 4 over 6
equals 2 over 3                                      equals fraction numerator 3 minus 1 over denominator 4 minus 1 end fraction
equals 2 over 3                                    equals fraction numerator 3 minus left parenthesis negative 3 right parenthesis over denominator 4 minus left parenthesis negative 5 right parenthesis end fraction
equals fraction numerator 3 plus 3 over denominator 4 plus 5 end fraction
equals 6 over 9
equals 2 over 3
    As the slope of all the three lines are same. So, they are collinear.

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