Answer:
[tex]y=-\dfrac{2}{5}x+4[/tex]
Step-by-step explanation:
A new corridor of the arena lies on the line [tex]y=\frac{5}{2}x.[/tex]
The slope of this new corridor is [tex]\frac{5}{2}.[/tex]
If [tex]m[/tex] is the slope of the prependicular line, then
[tex]\dfrac{5}{2}m=-1\\ \\m=-\dfrac{2}{5}[/tex]
Therefore, the perpendicularcorridor has the equation
[tex]y=-\dfrac{2}{5}x+b[/tex]
This corridor passes through the point (10,0), then
[tex]0=-\dfrac{2}{5}\cdot 10+b\\ \\b=4[/tex]
The equation of the corridor is
[tex]y=-\dfrac{2}{5}x+4[/tex]
