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Prove that the points (4,3),(1,4)and (-2...

Prove that the points `(4,3),(1,4)and (-2,5)` are collinear. Also find out the equation of the straight line on which these points lie.

Text Solution

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Let the points be `A(4,3),B(1,4)and C(-2,5).`
The equation of line passing through A and B is
`y-3=((4-3)/(1-4))(x-4)`
`impliesy-3=(-1)/(3)(x-4)`
`impliesx+3y-13=0`
Clearly, point C(1,4) satisfies the equation `x+3y-13=0.` Hence the given points lie on the same line whose equation is `x+3y-13=0.`
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