Let d be the distance from a point (x, y) on the line y = 11x − 8 to the point (0,0). Write d^2 as a function of x.

Question

hitaro9 · Answer

I also need to find the closest point on the line to 0,0.

anonymous · Answer

For the first question, the two points are (0,0) and (x, 11 x -8)
Apply the distance formula to find $d^2$

anonymous · Answer

$$
d^2=(x-0)^2+ (11x -8 -0)^2=122 x^2-176 x+64
$$

anonymous · Answer

Minimize the last answer with respect to x

anonymous · Answer

$$
g(x) = d^2=122 x^2-176 x+64\
g'(x)= 244x- 176\
g'(x) =0 \implies x =\frac{44}{61} \implies  y= 11 x -8 = -\frac 4{61}

$$

hitaro9 · Answer

Alright. Thank you. I'll see if that works. I appreciate the help.

anonymous · Answer

Did you understand it?

hitaro9 · Answer

Yeah. I think so. You're using the formula for distance between two points right?

hitaro9 · Answer

I haven't used that in forever. Hadn't thought of it.

anonymous · Answer

yes