MathCalculus
posted by Jacob
Find the point on the line 2x + 4y + 3 =0 which is closest to the point (2,1). Note: I have been struggling on this for hours!

Reiny
For hours ???
Slope of the given line is 1/2
so the slope of the line through (2,1) and perpendicular to it must be 2
equation of that perp.
y = 2x + b, with (2,1) lying on it, thus ...
1 = 2(2) + b
3 = b
y = 2x  3
solve the two equations to get the required point
2x + 4y + 3 = 0
2x + 4(2x3) + 3 = 0
2x 8x  12 + 3 = 0
10x = 9
x = 9/10
sub that back into y = 2x3
y = 2(9/10)  3 = 6/5
the point is (9/10 , 6/5) 
Jacob
Thank you very much Reiny for this wonderful explanation. I am not the brightest bulb and yes 2 hours to be precise.
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