Problem 4. Using vectors.

$\overline{H K}=\overline{A K}-\overline{A H}=\frac{1}{2}(\overline{A Q}+\overline{A N})-\frac{1}{2}(\overline{A M}+\overline{A P})=$

$=\frac{1}{2}\left(\frac{1}{2}(\overline{A E}+\overline{A D})+\frac{1}{2}(\overline{A B}+\overline{A C})\right)-$

$-\frac{1}{2}\left(\frac{1}{2} \overline{A B}+\frac{1}{2}(\overline{A C}+\overline{A D})\right)=\frac{1}{4} \overline{A E}$.

Therefore, $H K=\frac{1}{4} A E=1.75$.
Answer: 1.75.

![](https://cdn.mathpix.com/cropped/2024_05_06_1015c2cf6918084885d1g-1.jpg?height=540&width=691&top_left_y=1712&top_left_x=1231)