Question

Using the concept of slope, prove that the points (a, b +c), (b,c+a) and (c, a+b) are in a straight line.

Answer 1

Points A (a, b +c), B (b, c+a) and C (c, a+b) all lie on the same straight line So, slope of the line joining A and B is same as the slope of the line joining B and C. Let $m_1$ be the slope of the line joining A and B and $m_2$ be the slope of the line joining B and C.

$m_1=\frac{c+a-(b+c)}{b-a}=\left(\frac{a-b}{b-a}\right)=-1$
$m_2=\frac{a+b-(c+a)}{c-b}=\left(\frac{b-c}{c-b}\right)=-1$

Both the slopes are equal

Hence, they are collinear.