What renders points collinear?


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Points that space coplanar lie in the same plane. In the diagram below, point out A, B, U, W, X, and Z lie in plane M and points T, U, V, Y, and also Z lie in plane N.

You are watching: Points ab and c are collinear

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clues A, Z, and B space collinear. Likewise, points T, U, and also V room collinear since they lied on a distinctive line.Points X and also Y space collinear even though they lie in various planes. (It must be provided however, it is possible to construct a plane containing X and also Y.)Since friend can attract a line through any two points there are countless pairs of points that space collinear in the diagram.A set of clues that space non-collinear (not collinear) in the same airplane are A, B, and also X.A collection of clues that room non-collinear and in different planes room T, Y, W, and B.

Features of upright points

1. A suggest on a line that lies between two various other points ~ above the very same line have the right to be construed as the beginning of 2 opposite rays.

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Point C lies in between points A and B on ab (above). Using these points, we can type two opposite rays, CA and CB.

2. Segment lengths. The Segment enhancement Postulate states that if A, B, and C room points ~ above the very same line wherein B is between A and C, then abdominal + BC = AC.

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Example:

If (1, 2), (3, 6), and also (5, k) space collinear points, what is the worth of k?

We can discover the value of k by first finding the slope between the two known points. We can then deal with for k through equating the slope us just found to an expression because that the slope consisting of k together an unknown:

Using points (1, 2) and (3, 6) to discover the slope of the line, we get,

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The slope in between (3, 6) and also (5, k) is,

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Since the points space collinear the slopes for these 2 points room equal so,

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k = 10

Thus, the worth for k is 10 and also the coordinate of the third collinear suggest is (5, 10).