Question

Show that A(a,b+c),B(b,c+a) and C(c,a+b) are colinear

Answer 1

The three points A(a,b+c), B(b,c+a) and C(c,a+b) are colinear, it is proves.

Step-by-step explanation:

Here, A(x_1 = a, y_1 = b + c), B(x_2 = b, y_2 = c + a) and

C(x_3 = c, y_3 = a + b)

If the tree points are coinear, then area of triangle is zero.

∴ x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) = 0

⇒ a(c + a  - a - b) + b(a + b - b - c) + c(b + c - c - a) = 0

⇒ a(c - b) + b(a  - c) + c(b - a) = 0

⇒ ac - ab + ba  - bc + cb - ac = 0

⇒ 0 = 0, it is proved.