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

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) (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 , which means the slope of the perpendicular line is . So the equation of the perpendicular line is and now we need to solve for b. To do that, substitutue the ordered pair values (4,0) into the equation and get or b=10. So the final equation of the perpendicular line is and the graph of both lines is below.

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