What provides points collinear?
Points that room coplanar lie in the very same plane. In the diagram below, clues A, B, U, W, X, and also Z lied in plane M and also points T, U, V, Y, and also Z lied in plane N.
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Features of upright points
1. A point on a line the lies between two various other points on the very same line deserve to be taken 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 the contrary rays, CA and also CB.
2. Segment lengths. The Segment enhancement Postulate says that if A, B, and also C space points on the same line where B is between A and also C, then abdominal muscle + BC = AC.
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If (1, 2), (3, 6), and also (5, k) room collinear points, what is the value of k?
We can discover the value of k by very first finding the slope between the two known points. We have the right to then deal with for k by equating the slope we just found to one expression for the slope consisting of k together an unknown:
Using points (1, 2) and (3, 6) to uncover the slope of the line, we get,
The slope 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 value for k is 10 and the coordinate of the 3rd collinear suggest is (5, 10).