| Assertion (A): Centroid of a triangle formed by the points \[(a,b),\]\[(b,c)\] and \[(c,a)\] is at origin. Then \[\text{a}+\text{b}+c=0.\]. |
| Reason (R): Centroid of a \[\Delta ABC\] with vertices \[A({{x}_{1}},{{y}_{1}}),\] \[B({{x}_{2}},{{y}_{2}})\]and \[C({{x}_{3}},{{y}_{3}})\] is given by \[\left( \frac{{{x}_{1}}+{{x}_{2}}+{{x}_{3}}}{3},\,\,\frac{{{y}_{1}}+{{y}_{2}}+{{y}_{3}}}{3} \right)\] |
A) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)
B) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
C) Assertion (A) is true but reason (R) is false.
D) Assertion (A) is false but reason (R) is true.
Correct Answer: A
Solution :
| [a] Centroid of a triangle with vertices \[(a,b),\]\[(b,c)\] and \[(c,a)\]is \[\left( \frac{a+b+c}{3},\frac{b+c+a}{3} \right)=(0,0)\] |
| \[a+b+c=0\] |
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