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I can't believe they're making this a multiple choice question. What a wingspan move.

can you help me?

In this case those... \(x_1=-2\), \(x_2=x\), \(y_1=1\), \(y_2=y\).

I would do \(x_2=x=2y-4\) so that you have it all in one variable.

So we get \[
d(y) = \sqrt{((2y-4)-(-2))^2+((y)-(1))^2}=\sqrt{(2y-2)^2+(y-1)^2}
\]

ok

That needs to be simplified a bit.

\[
\sqrt{4y^2-8y+4+y^2-2y+1}=\sqrt{5y^2-10y+5}
\]

\[
d(y)=\sqrt{5(y-1)^2}=\sqrt{5}(y-1)
\]Now we want to minimize this distance function....

ok how do we do that?

We take the derivative and find some critical numbers!!

\[d'(y)=\sqrt{5} \]Wait what...

so the answer is 0?

awesome thanks!