Posted by **Morgan** on Tuesday, June 18, 2013 at 2:08pm.

Find the point on the line 4x+3y-4=0 which is closest to the point (5,2)

- Calculus -
**Steve**, Tuesday, June 18, 2013 at 3:13pm
A line from (5,2) perpendicular to the curve will have the shortest distance to the curve.

The slope of the graph is -4/3, so the normal has slope 3/4

So, now you have a point and a slope, so the perpendicular line through (5,2) is

y-2 = 3/4 (x-5)

y = 3/4 x - 7/4

These two lines intersect at (37/25,-16/25)

- Calculus -
**Morgan**, Tuesday, June 18, 2013 at 3:23pm
Thank you for your help!

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