### What renders points collinear?   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 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. 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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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, The slope in between (3, 6) and also (5, k) is, Since the points space collinear the slopes for these 2 points room equal so, k = 10

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