JEE Mains · Maths · STD 11 - rectangular cartensian co-ordinates
Let the vertex \(A\) of a triangle \(ABC\) be \((1, 2)\), and the mid-point of the side \(AB\) be \((5, -1)\). If the centroid of this triangle is \((3, 4)\) and its circumcenter is \((\alpha, \beta)\), then \(21(\alpha + \beta)\) is equal to:
- A \(309\)
- B \(403\)
- C \(497\)
- D \(524\)
Answer & Solution
Correct Answer
(C) \(497\)
Step-by-step Solution
Detailed explanation
Let the coordinates of vertex \(B\) be \((x_1, y_1)\) and vertex \(C\) be \((x_2, y_2)\). Since the mid-point of \(AB\) is \((5, -1)\), we have: \(\dfrac{1 + x_1}{2} = 5 \Rightarrow x_1 = 9\) \(\dfrac{2 + y_1}{2} = -1 \Rightarrow y_1 = -4\) Thus, \(B \equiv (9, -4)\). Given the…
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