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!

Answer 1

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(-2x-3) + 3 = 0
-2x -8x - 12 + 3 = 0
-10x = 9
x = -9/10
sub that back into y = -2x-3
y = -2(-9/10) - 3 = -6/5

the point is (-9/10 , -6/5)

Answer 2

Thank you very much Reiny for this wonderful explanation. I am not the brightest bulb and yes 2 hours to be precise.