B1. Accurately calculate the distance between the point $A(-1,-6)$ and the intersection of the lines $2 x+4 y-2=0$ and $x+3 y+1=0$. Provide the result in simplified radical form.
B1. First, we find the intersection of the lines by solving a system of two equations with two unknowns: $2 x+4 y-2=0$ and $x+3 y+1=0$. This has the solution $x=5, y=-2$, so the intersection is $P(5,-2)$. Using the distance formula between points, we calculate $d(P, A)=2 \sqrt{13}$.

Correct solving of the system .......................................................................................

![](https://cdn.mathpix.com/cropped/2024_06_07_4401d59a37898c9fd2b4g-12.jpg?height=55&width=1642&top_left_y=635&top_left_x=273)

![](https://cdn.mathpix.com/cropped/2024_06_07_4401d59a37898c9fd2b4g-12.jpg?height=54&width=1639&top_left_y=687&top_left_x=274)

Writing or using the distance formula: $d(A, P)=\sqrt{(-1-5)^{2}+(-6+2)^{2}} \ldots \ldots .1$ point

![](https://cdn.mathpix.com/cropped/2024_06_07_4401d59a37898c9fd2b4g-12.jpg?height=51&width=1637&top_left_y=791&top_left_x=278)

![](https://cdn.mathpix.com/cropped/2024_06_07_4401d59a37898c9fd2b4g-12.jpg?height=48&width=1636&top_left_y=841&top_left_x=276)