(a,-2),(a,3),(a,0) Determine whether the given set of points in each case are collinear or not
Answers
The given set of points (a,-2),(a,3),(a,0) in each case are collinear.
Step-by-step explanation:
Let the given set of points (a,-2), (a,3) & (a,0) be the vertices of triangle ABC such that
Coordinates of A = (x1,y1) = (a, -2)
Coordinates of B = (x2,y2) = (a, 3)
Coordinates of C = (x3,y3) = (a, 0)
We know that three points are collinear if and only if the area of the triangle ABC is zero.
So,
The formula for the area of ∆ABC is given as,
= ½ * [x1(y2-y3) + x2(y3-y1) + x3(y1-y2)]
substituting the values, we get
= ½ * [a(3-0) + a{0 - (-2)} + a(-2 - 3)]
= ½ * [ 3a + 2a - 5a]
= ½ * 0
= 0
∴ Area of ∆ABC = 0
⇒ Points A, B and C lie on the same line
⇒ A, B and C are collinear points.
Thus, the given set of points (a,-2),(a,3) & (a,0) are collinear.
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Determine if the following set of points are collinear or not.
(i) (4, 3), (1, 2) and (-2, 1) (ii) (-2, -2), (-6, -2) and (-2, 2)
(iii) 2 3 ` j - ,3 ,(6, -2) and (-3, 4)
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Answer:
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Step-by-step explanation:
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