Question

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Answer 1

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Answer and Step-by-step explanation:

Here the three coordinates given are=>(-1,-2);(5,2);(7/2,1)

Therefore,x₁=-1 ,x₂=5 ,x₃=7/2

        and, y₁=-2 ,y₂=2 ,y₃=1

We know that three points are collinear if the area of the triangle formed by their co-ordinates is 0.

So,now using formula of area of triangle[We are denoting it as A(Δ)] for given three coordinates:-

A(Δ)=1/2[x₁(y₂–y₃)+x₂(y₃–y₁) + x₃(y₁–y₂)]

Now, putting values,

A(Δ)=1/2[-1 (2-1) + 5 (1- (-2)) + 7/2 (-2- 2)]

A(Δ)=1/2[-1 (1)+5 (3)+7/2 (-4)]

A(Δ)=1/2[-1+15-14]

A(Δ)=1/2[0]

A(Δ)=0

Hence, the given coordinates are collinear as the area of the the triangle made by the coordinates is 0.

Hence proved

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