how will you determine that the given 3 point are collinear or not, using distance formula
Answers
Answer:
In general, three points A, B and C are collinear if the sum of the lengths of any two line segments among AB, BC and CA is equal to the length of the remaining line segment, that is, either AB + BC = AC or AC +CB = AB or BA + AC = BC.
Answer:
3 points that are A, B and C are collinear if the sum of the lengths of any two line segments among AB, BC and CA is equal to the length of the remaining line segment, that is, either AB + BC = AC or AC +CB = AB or BA + AC = BC.
Step-by-step explanation:
Let A, B and C be the three points.
We have to find the three lengths AB, BC and AC among the given three points A, B and C.
The three points A, B and C are collinear, if the sum of the lengths of any two line segments among AB, BC and AC is equal to the length of the remaining line segment.
That is,
AB + BC = AC
(or)
AB + AC = BC
(or)
AC + BC = AB
Example :
Using the concept of distance between two points, show that the points A(5, -2), B(4, -1) and C(1, 2) are collinear.
Solution :
We know the distance between the two points (x1, y1) and (x2, y2) is
d = √[(x2 - x1)2 + (y2 - y1)2]
Let us find the lengths AB, BC and AC using the above distance formula.
AB = √[(4 - 5)2 + (-1 + 2)2]
AB = √[(-1)2 + (1)2]
AB = √[1 + 1]
AB = √2
BC = √[(1 - 4)2 + (2 + 1)2]
BC = √[(-3)2 + (3)2]
BC = √[9 + 9]
BC = √18
BC = 3√2
AC = √ [(1 - 5)2 + (2 + 2)2]
AC = √ [(-4)2 + (4)2]
AC = √ [16 + 16]
AC = √32
AC = 4√2
Therefore, AB + BC = √2 + 3√2 = 4√2 = AC
Thus, AB + BC = AC
Hence, the given three points A, B and C are collinear.
hope it helps you