Question

(a,–2), (a,3), (a,0) Determine whether the given set of points in each case are collinear or not.

Answer 1

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Answer 2

Hi ,

Let A(a,-2),B(a,3),C(a,0) are vertices

of triangle ABC.

*************************************
If A(x1,y1),B(x2,y2), and C(x3,y3)

are three vertices of a triangle ABC

then

area (∆ABC )

=1/2|x1(y2-y3)+x2(y3-y1)+x3(y1-y2)|
************************************************

Here,

area (∆ABC )

= 1/2|a(3-0)+a[ 0 - (-2) ] + a(-2 - 3)|

=1/2| 3a + 2a - 5a |

= 1/2 × 0

= 0

Therefore ,

area ∆ABC = 0 .

A, B and C are lying on a line .

Then , they cannot form a triangle.

When the area of a triangle is zero

then the three points said to be

collinear points .

A , B and C are collinear points.

I hope this helps you.

: )