What are Colinear Points? | Geometry, Points and Lines
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4 سال پیش
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What are colinear points? We'll
What are colinear points? We'll be discussing them with examples and a practice problem in today's video lesson! We say that points are colinear if they lie on the same line.
A single point is always colinear with itself because it lies on the same lines as itself. Any two points are also colinear because 2 points will always define a unique line that passes through them both.
Thus, it is most comment that when we discuss colinear points we talk about at LEAST 3 points, because not all three points are colinear. If three or more points do all lie on the same line then they are colinear.
SOLUTION TO PRACTICE PROBLEM:
Since A, C, and B are colinear, and C is between A and B, we know that the distance from A to C (2x - 1) plus the distance from C to B (2x+2) must equal the distance from A to B. Thus, AC + CB = AB, so (2x-1) + (2x+2) = 13, thus 4x +1 = 13, hence 4x = 12 and therefore x = 3.
Note that if C was not colinear with A and B then we'd be dealing with a triangle situation, and solving the problem wouldn't be so easy, AB + CB would not be equal to AB, in fact AB + CB would HAVE to be GREATER than AB by the triangle inequality theorem.
I hope you find this video helpful, and be sure to ask any questions down in the comments!
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A single point is always colinear with itself because it lies on the same lines as itself. Any two points are also colinear because 2 points will always define a unique line that passes through them both.
Thus, it is most comment that when we discuss colinear points we talk about at LEAST 3 points, because not all three points are colinear. If three or more points do all lie on the same line then they are colinear.
SOLUTION TO PRACTICE PROBLEM:
Since A, C, and B are colinear, and C is between A and B, we know that the distance from A to C (2x - 1) plus the distance from C to B (2x+2) must equal the distance from A to B. Thus, AC + CB = AB, so (2x-1) + (2x+2) = 13, thus 4x +1 = 13, hence 4x = 12 and therefore x = 3.
Note that if C was not colinear with A and B then we'd be dealing with a triangle situation, and solving the problem wouldn't be so easy, AB + CB would not be equal to AB, in fact AB + CB would HAVE to be GREATER than AB by the triangle inequality theorem.
I hope you find this video helpful, and be sure to ask any questions down in the comments!
+WRATH OF MATH+
◆ Support Wrath of Math on Patreon: Patreon: wrathofmathlessons
Follow Wrath of Math on...
● Instagram: Instagram: wrathofmathedu
● Facebook: Facebook: WrathofMath
● Twitter: Twitter: wrathofmathedu
My Music Channel: seanemusic
4 سال پیش
در تاریخ 1399/01/20 منتشر شده
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