Posted by **Manny** on Wednesday, December 9, 2009 at 3:54am.

Find the point on the line 6x + y = 9 that is closest to the point (-3,1).

Solution: We need to minimize the function

d = sqrt((x − (−3))^2 + (y − 1)^2)

= sqrt((x + 3)^2 + (y − 1) ^2 )

and, since the point (x, y) lies on the line 6x + y = 9, we can eliminate y from the formula for d:

d = (x + 3)^2 + (9 − 6x − 1) ^2

= (x + 3)^2 + (8 − 6x)^2

It will be easier to minimize the square of the function:

D = d2 = (x + 3)^2 + (8 − 6x)^2

Then,

D

- Calculus -
**MathMate**, Wednesday, December 9, 2009 at 8:18am
Yes, continue this way, find the derivative of D with respect to x.

Equate the derivative to zero and solve for x.

Substitute x back into the line equation to find y.

Post you answer for checking if you wish.

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