SOLUTION: Find a number t such that the distance between (-2,2) and (3t,2t) is as small as possible.

Question 907680: Find a number t such that the distance between (-2,2) and (3t,2t) is as small as possible.
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Use the distance formula.

To minimize the distance squared, take the derivative of the distance squared and set it equal to zero.

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You could also do it geometrically.
(3t,2t) defines a line through the origin where
You could find the line perpendicular to that line through the point (-2,2).
Perpendicular lines have negative reciprocal slopes so the slope would be
Using the point slope form of a line,

So then finding the intersection of the two lines,

So then,

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