Question

Prove that the points (4,5); (6,-1) and (0,17) are collinear.

Answer 1

Answer:

Step-by-step explanation:

Please see the attachment below.

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Answer 2

The slope of all three points should be the same, so that the points are collinear (lying on the same line).
let:
m1 be the slope of points (4,5) and (6,-1)
$m1 \: = \: \frac{y2 \: - \: y1}{x2 \: - \: x1}$
which is
$m1 \: = \: \frac{ - 1 \: - 5}{6 - 4} = \frac{ - 6}{2 } = - 3$
m2 be the slope of points (6,-1) and (0,17)
$m2 = \frac{y2 \: - y1}{x2 \: - x1}$

which is
$m2 = \frac{17 + 1}{0 - 6} = \frac{18}{ - 6} = - 3$
where m1 = m2 ........i.e., slopes are same

therefore all three points are collinear