| If two vertices of a triangle are (5, 4) and \[(-\,\,2,4)\]and centroid is (5, 6), then third vertex is |
A) \[(12,10)\]
B) \[(12,10)\]
C) \[(-10,12)\]
D) \[(12,-10)\]
E) \[(-10,-12)\]
Correct Answer: A
Solution :
| Let third vertex be \[(x,y).\] |
| Coordinate of centroid \[=\left( \frac{{{x}_{1}}+{{x}_{2}}+{{x}_{3}}}{3},\frac{{{y}_{1}}+{{y}_{2}}+{{y}_{3}}}{3} \right)\] |
| Given, \[{{x}_{1}}=x,\]\[{{x}_{2}}=5,\]\[{{x}_{3}}=-\,\,2\] |
| \[{{y}_{1}}=y,\]\[{{y}_{2}}=4,\]\[{{y}_{3}}=4\]and centroid \[=(5,6)\] |
| \[\Rightarrow \]\[5=\frac{x+5-2}{3}\]\[\Rightarrow \]\[x=12\] |
| \[\Rightarrow \]\[6=\frac{y+4+4}{3}\]\[\Rightarrow \]\[y=10\] |
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