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Answer: \(PQ^2+QR^2=PR^2\), so ΔPQR is right angled at Q.

\[PQ^2=(2+2)^2+(2-2)^2=16\]

\[QR^2=(2-2)^2+(7-2)^2=25\]

\[PR^2=(2+2)^2+(7-2)^2=41\]

\(PQ^2+QR^2=16+25=41=PR^2\). By the converse of Pythagoras theorem, \(\angle PQR=90^\circ\), so P, Q, R are vertices of a right angled triangle.

Doubtly AI · 24 Oct 2026 AI-verified · Oct 2026 Report
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