Question:
The base of vertices of an isosceles triangle PQR are Q(1, 3) and R(-2, 7). The vertex P can be
The base of vertices of an isosceles triangle PQR are Q(1, 3) and R(-2, 7). The vertex P can be
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Equal sides condition gives equation of perpendicular bisector of QR.
Updated On: Apr 7, 2026
- (1, 6)
- (1/2, 5)
- (5/6, 6)
- None of these
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept:
In isosceles triangle, \(PQ = PR\).
Step 2: Detailed Explanation:
Let \(P = (x, y)\)
\((x - 1)^2 + (y - 3)^2 = (x + 2)^2 + (y - 7)^2\)
Simplify: \(-6x + 8y = 43\)
Check options: \((5/6, 6)\) satisfies.
Step 3: Final Answer:
\(P = (5/6, 6)\).
In isosceles triangle, \(PQ = PR\).
Step 2: Detailed Explanation:
Let \(P = (x, y)\)
\((x - 1)^2 + (y - 3)^2 = (x + 2)^2 + (y - 7)^2\)
Simplify: \(-6x + 8y = 43\)
Check options: \((5/6, 6)\) satisfies.
Step 3: Final Answer:
\(P = (5/6, 6)\).
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