### What renders points collinear?   Points that are coplanar lie in the exact same airplane. In the diagram below, points A, B, U, W, X, and Z lie in airplane M and also points T, U, V, Y, and Z lie in aircraft N.

You are watching: Any three distinct points are collinear Points A, Z, and B are collinear. Likewise, points T, U, and V are collinear since they lie on a unique line.Points X and also Y are colstraight even though they lie in different planes. (It have to be detailed yet, it is feasible to construct a plane containing X and also Y.)Since you deserve to draw a line through any kind of 2 points tright here are numerous pairs of points that are collinear in the diagram.A set of points that are non-coldirect (not collinear) in the same airplane are A, B, and X.A collection of points that are non-colstraight and also in various planes are T, Y, W, and also B.

## Features of colstraight points

1. A suggest on a line that lies in between 2 other points on the very same line have the right to be interpreted as the origin of two opposite rays. Point C lies in between points A and B on AB (above). Using these points, we can develop 2 opposite rays, CA and CB.

2. Segment lengths. The Segment Addition Postulate says that if A, B, and also C are points on the same line wright here B is in between A and also C, then AB + BC = AC.

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If (1, 2), (3, 6), and (5, k) are coldirect points, what is the value of k?

We can uncover the worth of k by first finding the slope between the 2 known points. We can then deal with for k by equating the slope we simply discovered to an expression for the slope consisting of k as an unknown:

Using points (1, 2) and also (3, 6) to uncover the slope of the line, we get, The slope between (3, 6) and (5, k) is, Because the points are colstraight the slopes for these 2 points are equal so, k = 10

Therefore, the worth for k is 10 and also the coordinate of the third colstraight allude is (5, 10).