Question

The area of the triangle formed by the points (a, b + c), (b,c + a), (C, a + b) is:

Answer 1

Answer:

Step-by-step explanation:

$The\;area\;of\;a\;triangle\;formed\;by\;the\;points\\\\A(x_1,y_1)\;B(x_2,y_2)\;C(x_3,y_3)\\is\;given\;by\\=\left|\begin{array}{ccc}x_1&x_2&x_3\\y_1&y_2&y_3\\1&1&1\end{array}\right|$

Given

A(a , b + c)  B(b . c + a) C(c , a+b)

The Area of Trg ABC is

$=\left|\begin{array}{ccc}a&b&c\\b+c&c+a&a+b\\1&1&1\end{array}\right|\\R_1--->R_1+R_2\\=\left|\begin{array}{ccc}a+b+c&a+b+c&a+b+c\\b+c&c+a&a+b\\1&1&1\end{array}\right|\\\\=(a+b+c)\left|\begin{array}{ccc}1&1&1\\b+c&c+a&a+b\\1&1&1\end{array}\right|\\\\=(a+b+c)(0)\\\\since \;2\;rows\;are\;same\;det=0\\\\=\;0$

Therefore the Area of Triangle ABC is 0.

=> A , B , C are colinear points.

Hope it Helps