Question

show that the points (a, b+c) , (b,c+a) and (c, a+b) are colinear.

Answer 1

Answer:

Hope this helps.

The gradient of the line joining (a, b+c) to (b, c+a) is

[ ( c+a ) - ( b+c ) ] / ( b - a )  =  ( a - b ) / ( b - a ) = -1

The gradient of the line joining (a, b+c) to (c, a+b) is

[ ( a+b ) - ( b+c ) ] / ( c - a )  =  ( a - c ) / ( c - a ) = -1

As these lines have the same gradient and they both pass through the point (a, b+c), they are the same line.

That is, the three points are collinear.