DIRECTION: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
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
Assertion: Centroid of a triangle formed by the points (a, b), (b, c) and (c, a) is at origin, Then \( a+b+c=0 \).
Reason: Centroid of a \( \triangle P Q R \) with vertices \( \mathrm{P}\left(\mathrm{x}_{1}, \mathrm{y}_{1}\right), \mathrm{B}\left(\mathrm{x}_{2}, \mathrm{y}_{2}\right) \) and \( \mathrm{R}\left(\mathrm{x}_{3}, \mathrm{y}_{3}\right) \) is given by \( \left(\frac{x_{1}+x_{2}+x_{3}}{3}, \frac{y_{1}+y_{2}+y_{3}}{3}\right) \).
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