A) (7, 4)
B) (8, 14)
C) (12, 21)
D) None of these
Correct Answer: D
Solution :
Given, O (0, 0) is the orthocenter. Let A (h, k) be the third vertex, B\[(-\,\,2,3),\]and C\[(5,-1)\]the other two vertices. Then the slope of the line through A and O is k / h, while the lines through B and C has the slope \[-\,\,4/7.\] By the property of the orthocenter, these two lines must be perpendicular, so we have |
\[(\text{k/h})\left( -\frac{4}{7} \right)=-1\]\[\Rightarrow \]\[\text{k/h}=\frac{7}{4}\] ?(i) |
Also, \[\frac{5-2+h}{3}+\frac{-1+3+k}{3}=7\] |
\[\Rightarrow \] \[h+k=16\] ?(ii) |
Which is not satisfied by the points given in , or . |
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