Distance formula with $(0,0)$

Question

I am trying to work out the distance between two points: $(0,0)$ and $(5,-5)$. Using the distance formula give's me an answer of $0$ which is not right.

For example: $$ (0 - 5)^2 + (0 - (-5))^2) = (-25) + (25) = 0 $$ Am I missing something?

Answer 1

The distance between $(a_1,a_2)$ and $(b_1,b_2)$ is $$\sqrt{(a_1-b_1)^2+(a_2-b_2)^2}$$ So it should be: $$\sqrt{(0-5)^2+(0-(-5))^2}=\sqrt{(-5)^2+(5)^2}=\sqrt{25+25}=\sqrt{50}$$ Your mistake is that $(-5)^2 \neq -25$, but $(-5)^2=25$.