what are the coordinates of the point on the line 7x-3y=11 that is closest to the origin? should i just let x= 0 and solve for y and then let y=0 and solve for x and get (x,y)?

a) (1.57, 0)
b) (1.33, 0.47)
c) (1.33. -0.57)
d) (1.43, -0.47)
e) (1.27, -0.67)

Question

what are the coordinates of the point on the line 7x-3y=11 that is closest to the origin? should i just let x= 0 and solve for y and then let y=0 and solve for x and get (x,y)?

a) (1.57, 0)
b) (1.33, 0.47)
c) (1.33. -0.57)
d) (1.43, -0.47)
e) (1.27, -0.67)

dumbcow · Answer

find the equation of line perpendicular to given line that goes through origin.
point where these 2 lines intersect is answer

myininaya · Answer

d=sqrt((x-0)^2+(y-0)^2) where (x,y) is a point on y=7x/3-11/3
d=sqrt(x^2+y^2)
d=sqrt(x^2+(7x/3-11/3)^2)
d^2=x^2+(7x/3-11/3)^2
f(x)=x^2+(7x/3-11/3)^2
find f'(x) to minimize

myininaya · Answer

attachment

myininaya · Answer

if x=77/58, then y=(7/3)*(77/58)-11/3