Question

Answer it I will mark you as brainalist answer​

Answer 1

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.