2025 Jurongville Secondary School Prelims A Math Paper 1
Find the equation of the perpendicular bisector of the points \(P(a, 4)\) and \(Q(6, -2)\) in terms of \(a\).[4]
The perpendicular bisector of line segment \(PQ\) passes through the point \(R(2, 1)\). Find the possible values of \(a\).[2]
\(S\) is the reflection of point \(Q\) across the perpendicular bisector of \(PQ\). By using the positive value of \(a\) found in part (b) calculate the area of the quadrilateral \(PQRS\).[4]
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Answer:(a) \(2(6-a)x-12y+a^2-24=0\). (b) \(a=6\) or \(a=-2\). (c) \(S=P\), so there is no non-degenerate quadrilateral; triangle \(PQR\) has area \(12\text{ units}^2\).