Question

Show that thd points A (a,b+c), B (b,c+a) and C (c,a+b) are collinear. This from the chapter of coordinate geometry......plzz who will give correct answer i will mark brainlist.....

Answer 1

Three or more points that lie on a same straight line are called collinear points.

With three points A, B and C, three pairs of points can be formed, they are: AB, BC and AC.

If Slope of AB = slope of BC = slope of AC, then A, B and C are collinear points.

Let ; A = (a, b+c), B = (b, c+a), C = (c, a+b)

Slope of AB
$m1= \frac{ b + c - (c + a)}{a - b} \\ = \frac{ - (a - b)}{(a - b)} = - 1$
Slope of BC
$m2 = \frac{ c + a - (a + b)}{b - c} \\ = \frac{ - (b - c)}{(b - c)} = - 1$
Slope of CA
$m3= \frac{ a + b- (b + c)}{c - a} \\ = \frac{ - (c - a)}{(c - a)} = - 1$
$m1 = m2 = m3$
Therefore the given points are colinear.