SOLUTION: Hi, I'm currently doing very poorly in Geometry, but my teacher gave us this problem for extra credit. It's due tomorrow (11/20/06) so if you could get back to me as soon as you ca

Algebra ->  Length-and-distance -> SOLUTION: Hi, I'm currently doing very poorly in Geometry, but my teacher gave us this problem for extra credit. It's due tomorrow (11/20/06) so if you could get back to me as soon as you ca      Log On


   

Question 62108: Hi, I'm currently doing very poorly in Geometry, but my teacher gave us this problem for extra credit. It's due tomorrow (11/20/06) so if you could get back to me as soon as you can, that'd be fantastic.

Find the shortest distance from the point (4,0) to the line -2x + 5y = 15.
Thank you so much!!
Answer by rchill(405) About Me  (Show Source):
You can put this solution on YOUR website!
The shortest distance is going to be a perpendicular line from that point to the given line. The slope of that perpendicular line is the opposite of the reciprical of the slope of the given line. Solving for y in order to get the equation of a line in y=mx+b, where m is the slope and b is the y-intercept, we get y=expr%282%2F5%29x%2B3, which means the slope of the perpendicular line is -expr%285%2F2%29. So the equation of the perpendicular line is y=-expr%285%2F2%29x%2Bb and now we need to solve for b. To do that, substitutue the ordered pair values (4,0) into the equation and get 0=-expr%285%2F2%294%2Bb or b=10. So the final equation of the perpendicular line is y=-expr%285%2F2%29x%2B10 and the graph of both lines is below.
graph%28200%2C200%2C-5%2C5%2C-5%2C5%2C2x%2F5%2B3%2C-5x%2F2%2B10%29