Find the point on the line 3x + 2y -3 = 0, which is closest to the point (1, -3).

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- Nov 5th 2009, 11:51 AMB-lapFind the point on the line 3x + 2y -3 = 0, which is closest to the point (1, -3)
Find the point on the line 3x + 2y -3 = 0, which is closest to the point (1, -3).

( , ) ? - Nov 5th 2009, 12:03 PMPlato
- Nov 5th 2009, 12:05 PMJameson
Call this point (a,b). Solve line equation for y. Now use the distance formula between the point (1,-3) and (a,b).

Two hints: 1) (a,b) = (a,f(a)) where f(a) is the y-value for x=a

2) The distance formula has a nasty square-root. If you minimize D^2, you also minimize D. So you can drop the square root.

Differentiate and find critical point.