Question

Determine if points (2,5) (4,6) and (-2,-4) are collinear.​

Answer 1

$\sf \sqrt{(x_2 \: - x_1)^{2} + {(y_2 - y_1)}^{2} } \\ \sf = \sqrt{ {(4 - 2)}^{2} + {(6 - 5)}^{2} } \\ \sf = \sqrt{ {2}^{2} + {1}^{2} } \\ \sf = \sqrt{5} \: units$

while,

$\sf \sqrt{(x_3 \: - x_2)^{2} + {(y_3- y_2)}^{2} } \\ \sf = \sqrt{ {( - 2 + 4)}^{2} + {( - 4 + 6)}^{2} } \\ \sf = \sqrt{ {2}^{2} + {2}^{2} } \\ = \sf \sqrt{8} \\ \sf = 2 \sqrt{2} \: units$

The Given points are not collinear because the distance between them is not equal .

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