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The diagonals of a square of side 4 lie on the axes and its center at the origin. Find the coordinates of its vertices.
Solution:
If the center of a square is located at the origin, then the diagonals will be bisected into equal parts. Since the diagonals are located along the axes, then the sides of a square will be the hypotenuse of the four isosceles right triangles. To illustrate the problem, it is better to draw the figure as follows
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| Photo by Math Principles in Everyday Life |
Consider the right triangle at the first quadrant and apply Pythagorean Theorem, we have
Therefore, the coordinate of the vertices are
