Question

Can someone please help with this question

Find the closest point on the line y=2x to (1,0)

Answer 1

the closest point between two spots is a straight line that is perpendicular to it. right?

Answer 2

yes

Answer 3

then lets make a line perpendicular to this one the crosses thru the point (1,0)

Answer 4

then where those lines meet is the nearest point right?

Answer 5

y = 2x; y = (-1/2)x is perpendicular to it.

Answer 6

0 = (-1/2)(1) + b

0 = -1/2 + 1/2

our equation is going to be y = (-1/2)x + 1/2

Answer 7

now where do these two equations meet up?

y = 2x
y = (-1/2)x + 1/2


2x = (-1/2)x + 1/2

2x + (1/2)x = 1/2

(5/2)x = 1/2
---- ---
5/2 5/2

x = 1/5

the nearest point is: (1/5 , 2,5)

Answer 8

(1/5 , 2/5) if I can type today :)

Answer 9

y = (-1/2)(1/5) + 1/2

y = -1/10 + 5/10

y = 4/10 = 2/5 that chacks out good :)

Answer 10

you agree?

Answer 11

yes I do

Answer 12

good :) but I hope you do so because its right, and not becasue I said so ;)

Answer 13

Thanks