Three identical coins, labeled A, B, and C in the figure, lie on three corners of a square 10.0 cm on a side. Determine the x coordinate of each coin, xA, xB, and xC.
The line of symmetry of the triangle bisects the right angle and the diagonal of the square. The line is 1/2 the length of the square's diagonal :
(1/2)(10√2) = 5√2.
Let CG be a distance x from the vertex of the right angle in the triangle. Remaining distance = 5√2 - x. (1)(x) = (2)(5√2 - x) x = 10√2 - 2x 3x = 10√2 x = (10/3)√2.
Using Pythagorean theorem, x^2 + y^2 = c^2
c = (10/3)√2, and x = y, so 2x^2 = 200/9 x = √(100/9) = 10/3 = y.
