Draw a ray diagram with Python

A toy $4\ \text{cm}$ tall stands $27\ \text{cm}$ in front of a concave mirror of focal length $15\ \text{cm}$. You will make the program find the image from the mirror formula, find its height, and say if it is real or virtual. Then it draws the two rays and the image.

The idea. With the signs, $u = -27\ \text{cm}$ and $f = -15\ \text{cm}$. Then $\dfrac{1}{v} = \dfrac{1}{f} - \dfrac{1}{u}$ and $h' = -\dfrac{v}{u} \times h$.

Your tasks.

1. Work out v, the image distance, in cm.
2. Work out h_image, the height of the image, in cm (negative means inverted).
3. Set kind to "real" or "virtual", from the sign of v.