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)
\[RD = \sqrt{\left( 0 - 2 \right)^2 + \left( 3 - 1 \right)^2}\]
\[RD = \sqrt{\left( 0 - 2 \right)^2 + \left( 3 - 1 \right)^2}\]
\[ = \sqrt{\left( - 2 \right)^2 + 2^2} = \sqrt{4 + 4}\]
\[ = 2\sqrt{2}\]
\[DS = \sqrt{\left( 2 - 3 \right)^2 + \left( 1 - \left( - 1 \right) \right)^2}\]
\[ = \sqrt{\left( - 1 \right)^2 + 4} = \sqrt{1 + 4}\]
\[ = \sqrt{5}\]
\[RS = \sqrt{\left( 0 - 3 \right)^2 + \left( 3 - \left( - 1 \right) \right)^2}\]
\[ = \sqrt{9 + 16}\]
\[ = \sqrt{25}\]
\[ = 5\]
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)