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Show that pointsA (a , b + c), B (b , c ...

Show that points`A (a , b + c)`, `B (b , c + a)`, `C (c , a + b)`are collinear.

Text Solution

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`"Area of "DeltaABC=1/2|{:(a,b+c,1),(b,c+a,1),(c,c+b,1):}|`
`=1/2|{:(a,a+b+c,1),(b,a+b+c,1),(c,a+b+c,1):}|(C_(2)toC_(2)+C_(1))`
`=1/2(a+b+c)|{:(a,1,1),(b,1,1),(c,1,1):}|`
`1/2(a+b+c)xx0`
`(becauseC_(1)" and "C_(3)" are same)`
`therefore A,B and C are collinear.
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