700. Find the distance from the point $(x, y)$ to the line $y=x$.
$\triangleright$ Vertically, this distance is equal to $|y-x|$ (see the figure). But the shortest distance will be the perpendicular dropped to the line. In a right triangle with angles of $45^{\circ}$, the leg is $\sqrt{2}$ times shorter than the hypotenuse, so the answer will be $|y-x| / \sqrt{2}$. $\triangleleft$

![](https://cdn.mathpix.com/cropped/2024_05_21_90703b5d5e76e3b5cd3dg-208.jpg?height=357&width=379&top_left_y=544&top_left_x=1341)

## A few more problems