AP EAMCET · Maths · Straight Lines
If \(O, G, S\) are respectively the orthocentre, centroid and circumcentre of a triangle whose vertices are \(A(2,3), B(2,4)\) and \(C(4,3)\), then \(A O^2+9 B G^2+4 C S^2=\)
- A \(\frac{77}{36}\)
- B 13
- C \(\frac{8}{9}\)
- D \(\frac{5}{4}\)
Answer & Solution
Correct Answer
(B) 13
Step-by-step Solution
Detailed explanation
Coordinate of vertices of triangle \[ \begin{aligned} & A(2,3), B(2,4), C(4,3) \\ & \therefore \quad A B=1, B C=\sqrt{5}, C A=2 \end{aligned} \] So, \(\triangle A B C\) is right angle triangle where right angle at \(A\) that is orthocentre also. Coordinate of orthocentre is…
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