B2. Points $A(2,-1), B(-1,-5)$, and $C(-3,-13)$ are the vertices of triangle $ABC$. Calculate the length of the median to side $BC$. The result should be exact and partially in radical form. Reflect points $A$ and $B$ over the x-axis. Denote the resulting points as $A'$ and $B'$. Draw quadrilateral $AA'B'B$ and calculate its area.

![](https://cdn.mathpix.com/cropped/2024_06_07_7e68135e1a71f8c81168g-04.jpg?height=1017&width=1036&top_left_y=588&top_left_x=547)
B2.

![](https://cdn.mathpix.com/cropped/2024_06_07_7e68135e1a71f8c81168g-19.jpg?height=1037&width=1039&top_left_y=1700&top_left_x=520)
Writing the coordinates of the midpoint of side $B C: R(-2,-9)$ ..... 1 point
Determination that the length of the median is equal to the distance between points $A$ and $R$ ..... 1 point
Calculation of the length of the median $t_{B C}=d(A, R)=\sqrt{(-2-2)^{2}+(-9+1)^{2}}$ ..... 1 point
Writing the solution $t_{B C}=4 \sqrt{5}$ ..... 1 point
Reflecting points $A$ and $B$ and drawing quadrilateral $A A^{\prime} B^{\prime} B$ ..... 1 point

1. method
Using the formula for the area of a trapezoid $S=\frac{a+c}{2} \cdot v=\frac{10+2}{2} \cdot 3$ ..... 2 points
Writing the solution $S=18$ ..... 1 point
2. method
Using the formula for the area of a triangle or the area of a rectangle and a right triangle ..... 2 points
Writing the solution $S=18$ ..... 1 point