JEE Mains · Maths · STD 11 - 9. straight line
In an equilateral triangle \(PQR\), let the vertex \(P\) be at \((3, 5)\) and the side \(QR\) be along the line \(x + y = 4\). If the orthocentre of the triangle \(PQR\) is \((\alpha, \beta)\), then \(9(\alpha + \beta)\) is equal to:
- A \(16\)
- B \(27\)
- C \(36\)
- D \(48\)
Answer & Solution
Correct Answer
(D) \(48\)
Step-by-step Solution
Detailed explanation
In an equilateral triangle, the orthocentre coincides with the centroid. The centroid divides the altitude from the vertex to the opposite side in the ratio \(2:1\). Let \(M\) be the foot of the perpendicular from \(P(3, 5)\) to the line \(QR\) given by \(x + y - 4 = 0\). The…
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