| Assertion (A): The coordinates of the centroid of a triangle whose vertices are \[(0,6),\] \[(8,12)\] and \[(8,0)\] are \[\left( \frac{17}{3},5 \right)\]. |
| Reason (R): Coordinates of the centroid of a triangle whose vertices are \[({{x}_{1}},{{y}_{1}}),\]\[({{x}_{2}},{{y}_{2}})\] and \[({{x}_{3}},{{y}_{3}})\] are \[\left( \frac{{{x}_{1}}+{{x}_{2}}+{{x}_{3}}}{3},\frac{{{y}_{1}}+{{y}_{2}}+{{y}_{3}}}{3} \right)\]. |
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: D
Solution :
| [d] Reason is clearly true. |
| Now, coordinate of the centroid of a triangle with vertices \[(0,6),\] \[(8,12)\]and \[(8,0)\] are |
| \[\left( \frac{0+8+8}{3},\,\,\frac{6+12+0}{3} \right)=\left( \frac{16}{3},6 \right)\] |
| \[\therefore \] Assertion [a] is false but reason (R) is true. |
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