Question

Plans for an arena map for a popular video game are drawn on a coordinate grid. a new corridor of the arena lies on the line y=5/2x. a perpendicular corridor passes through the point (10,0). Write the equation of the line that contains the new corridor.

y= 5/2x - 25
y = -2/5x + 4
y = 2/5x - 4
y = -5/2x + 5

Answer 1

`y=-(2)/(5)x+4`

Explanation:

A new corridor of the arena lies on the line
`y=(5)/(2)x.`

The slope of this new corridor is
`(5)/(2).`

If
`m` is the slope of the prependicular line, then

`(5)/(2)m=-1\\ \\m=-(2)/(5)`

Therefore, the perpendicularcorridor has the equation

`y=-(2)/(5)x+b`

This corridor passes through the point (10,0), then

`0=-(2)/(5)\cdot 10+b\\ \\b=4`

The equation of the corridor is

`y=-(2)/(5)x+4`