Question

The points (3, −2) (−2, 8) and (0, 4) are three points in a plane. Show that these points are collinear.

Answer 1

Hii friend.

Here is your answer.

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Answer 2

Answer:

Those given points are collinear. (Proved)

Step-by-step explanation:

Let us assume that there are three points on the coordinate plane namely A(x1, y1), B(x2,y2), and C(x3,y3).

Now, if the points A, B, and C are points on the same straight line i.e. those points are collinear, then the area of the triangle formed by those three points will be zero i.e 1/2[x1(y2-y3) +x2(y3-y1) +x3(y1-y2)] =0.

In this problem the points are, (3,-2), (-2,8) and (0,4).

So, area of Δ formed by joining those three points will be

=1/2[3(8-4) -2(4+2) +0(-2-8)]

=1/2{12-12}

=0

Hence, those given points are collinear. (Proved)