Find the point on the line -4x+2y+4=0 which is closest to the point (0,2).

Question

Please help!! thank you

Answer 1

You basically need to find the perpendicular to the given line passing through (0,2) then find the point of intersection.

So

-4x + 2y + 4 = 0

2y = 4x - 4

y = 2x - 2, slope 2

So perpendicular has slope -1/2

y = -1/2 x + b

x = 0, y = 2

so b = 2

So perpendicular is y = -1/2x + 2

y = 2x -2

-1/2x + 2 = 2x - 2

-(5/2)x = -4

x = 8/5

y = 16/5 - 2 = 6/5