Determine whether the given set of points in each case are collinaer or not. (a,-2),(a,3),(a,0)
Answers
Answer: 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.
hope it will help you
pls mark as brain list