Shortest distance between two points (one unknown?)

[DanielJackins]

1. The problem statement, all variables and given/known data

Find an equation of the line, say y=mx+b, which passes through the point (6,−2) and is perpendicular to the line −2x+4y=0

y=

What is the shortest distance from the point (6,−2) to the line −2x+4y=0?

2. Relevant equations

?

3. The attempt at a solution

So I found the equation of the line - 4y = 2x, y = 1/2x so the slope of the line it is perpendicular to is 1/2. So the line in question has a slope of -2. Subbed in the point (6,-2) and the slope to solve for b, and came up with the equation y = -2x + 10. Now I'm stumped on the second part of the question. I know the distance formula but how do I figure out the second point?

Thanks

[Bohrok]

Imagine a point somewhere above a line, say the x-axis. Imagine different lines going from the point to different points on the x-axis. Which one of those will be the shortest distance between the point and the x-axis? What's the relationship between their slopes?

[HallsofIvy]

1. The problem statement, all variables and given/known data

Find an equation of the line, say y=mx+b, which passes through the point (6,−2) and is perpendicular to the line −2x+4y=0

y=

What is the shortest distance from the point (6,−2) to the line −2x+4y=0?

2. Relevant equations

?

3. The attempt at a solution

So I found the equation of the line - 4y = 2x, y = 1/2x so the slope of the line it is perpendicular to is 1/2. So the line in question has a slope of -2. Subbed in the point (6,-2) and the slope to solve for b, and came up with the equation y = -2x + 10. Now I'm stumped on the second part of the question. I know the distance formula but how do I figure out the second point?

Thanks
The "shortest distance" from a point to a line is always perpendicular to that line. Where does your line y= -2x+ 10 intersect y= (1/2)x?

[DanielJackins]

Thanks for the help. I got the answer, my graphing calculator was throwing me off for some reason.