Coordinate Geometry Question 112
Question: The area of the triangle formed by the points $ (a,b+c),(b,c+a),(c,a+b) $ is
[IIT 1963; EAMCET 1982; RPET 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 $ =\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 & a+b+c & 1 \\ b & a+b+c & 1 \\ c & a+b+c & 1 \\ \end{vmatrix} $ (Applying $ C_2\to C_1+C_2) $
$ =\frac{(a+b+c)}{2}\begin{vmatrix} a & 1 & 1 \\ b & 1 & 1 \\ c & 1 & 1 \\ \end{vmatrix}=0 $ . Note : Students should remember this question as a fact.
BETA
