A) \[({{x}_{4}},\,\,-{{y}_{4}})\]
B) \[({{x}_{4}},\,\,{{y}_{4}})\]
C) \[(-{{x}_{4}},\,\,-\,{{y}_{4}})\]
D) \[(-{{x}_{4}},\,\,{{y}_{4}})\]
Correct Answer: C
Solution :
Centre of circle through P, Q, R and S can be given as \[\left( \frac{{{x}_{1}}+{{x}_{2}}+{{x}_{3}}+{{x}_{4}}}{2},\,\,\frac{{{y}_{1}}+{{y}_{2}}+{{y}_{3}}+{{y}_{4}}}{2} \right)\]and centroid of triangle PQR is \[\left( \frac{{{x}_{1}}+{{x}_{2}}+{{x}_{3}}}{3},\,\,\frac{{{y}_{1}}+{{y}_{2}}+{{y}_{3}}}{3} \right)\] hence orthocenter is \[(-{{x}_{4}},\,\,-{{y}_{4}}).\]You need to login to perform this action.
You will be redirected in
3 sec