Math  /  Geometry

QuestionFind the coordinates of point CC in right isosceles triangle ABC\triangle ABC where A(2,3)A(2,3) and B(7,3)B(7,3).

Studdy Solution
Calculate the coordinates of C.
C=(2,3+522),(2,3522)C = (2,3 + \frac{5\sqrt{2}}{2}), (2,3 - \frac{5\sqrt{2}}{2})C2=(7,3+522),(7,3522)C2 = (7,3 + \frac{5\sqrt{2}}{2}), (7,3 - \frac{5\sqrt{2}}{2})However, since AB\overline{\mathrm{AB}} is the hypotenuse, we discard the points (2,3+522)(2,3 + \frac{5\sqrt{2}}{2}) and (7,3+522)(7,3 + \frac{5\sqrt{2}}{2}).
The possible coordinates of C are (2,3522)(2,3 - \frac{5\sqrt{2}}{2}) and (7,3522)(7,3 - \frac{5\sqrt{2}}{2}).

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