Points $ A(1,2) $ and $ B(7,8) $ are plotted on the coordinate plane. Point $ C $ lies on the line $ y = -x + 10 $ and the triangle $ ABC $ is right‑angled at $ C $. If $ C $ is in the first quadrant and has $ x5 $, find the coordinates of $ C $.

Question

Points $ A(1,2) $ and $ B(7,8) $ are plotted on the coordinate plane. Point $ C $ lies on the line $ y = -x + 10 $ and the triangle $ ABC $ is right‑angled at $ C $. If $ C $ is in the first quadrant and has $ x>5 $, find the coordinates of $ C $.

Accepted Answer

$ \left( \frac{9+\sqrt{35}}{2},\; \frac{11-\sqrt{35}}{2} \right) $

Neco 2017 Mathematics Question 47

Points \( A(1,2) \) and \( B(7,8) \) are plotted on the coordinate plane. Point \( C \) lies on the line \( y = -x + 10 \) and the triangle \( ABC \) is right‑angled at \( C \). If \( C \) is in the first quadrant and has \( x>5 \), find the coordinates of \( C \).

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