Determine whether the points are collinear. A(1, -3), B(2, -5), C(-4, 7)
Answer:-
R(0, 3), D(2, 1), S(3, –1)
[RD = sqrt{left( 0 – 2 right)^2 + left( 3 – 1 right)^2}]
[RD = sqrt{left( 0 – 2 right)^2 + left( 3 – 1 right)^2}]
[ = sqrt{left( – 2 right)^2 + 2^2} = sqrt{4 + 4}]
[ = 2sqrt{2}]
[DS = sqrt{left( 2 – 3 right)^2 + left( 1 – left( – 1 right) right)^2}]
[ = sqrt{left( – 1 right)^2 + 4} = sqrt{1 + 4}]
[ = sqrt{5}]
[RS = sqrt{left( 0 – 3 right)^2 + left( 3 – left( – 1 right) right)^2}]
[ = sqrt{9 + 16}]
[ = sqrt{25}]
[ = 5]
Sum of two sides is not equal to the third side.
Hence, the given points are not collinear.
Chapter 5. Co-ordinate Geometry – Practice Set 5.1 (Page 107)