Question

Show that the three points (4,5) , (6, -1), and (0, 17) are collinear

Answer 1

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Answer 2

The three points (4,5) , (6, -1), and (0, 17) are collinear

Solutions:

If three points $(x_1, y_1), (x_2, y_2) , (x_3, y_3)$ are collinear then

$x_1(y_2 - y_3) + x_2( y_3 - y_1)+ x_3(y_1 - y_2) = 0$

From given,

$(x_1, y_1) = (4, 5)\\\\(x_2, y_2) = (6, -1)\\\\(x_3, y_3) = (0, 17)$

Substituting we get,

$4(-1-17) + 6 (17 - 5) + 0(4 + 1) = 0\\\\4 \times -18 + 6 \times 12 + 0 = 0\\\\-72 + 72 + 0 = 0\\\\0 = 0$

Thus the three points (4,5) , (6, -1), and (0, 17) are collinear

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