Coordinate Geometry Question 170
Question: The area of triangle formed by the points $ (a,b+c), $
$ (b,c+a), $
$ (c,a+b) $ is equal to
[Pb. CET 2003]
Options:
A) $ abc $
B) $ a^{2}+b^{2}+c^{2} $
C) $ ab+bc+ca $
D) 0
Show Answer
Answer:
Correct Answer: D
Solution:
Area of triangle $ =\frac{1}{2} \begin{vmatrix} a & b+c & 1 \\ b & c+a & 1 \\ c & a+b & 1 \\ \end{vmatrix} $
$ =\frac{1}{2}| \begin{vmatrix} a+b+c & b+c & 1 \\ b+c+a & c+a & 1 \\ c+a+b & a+b & 1 \\ \end{vmatrix} $
$ =\frac{1}{2}(a+b+c) \begin{vmatrix} 1 & b+c & 1 \\ 1 & c+a & 1 \\ 1 & a+b & 1 \\ \end{vmatrix} =0 $ .
BETA
