Question

Point E is located at (–2, 2) and point F is located at (4, –6). What is the distance between points E and F?

Answer 1

Hey, to get a distance in 2-dimensional space you can use the theorem of pythagoras: \[
c = \sqrt{a^2 +b^2}
\]
You can use this method for any \(n\)-dimensional space you have to add the squares of each dimension and take the square root.
For your problem you first need the vector from one point to another. You can simply do this by subtracting them:
\[
\begin{pmatrix}
-2 \\2
\end{pmatrix}-
\begin{pmatrix}
4 \\-6
\end{pmatrix} =
\begin{pmatrix}
-2 -4 \\-2-(-6)
\end{pmatrix}=
\begin{pmatrix}
-6\\4
\end{pmatrix}
\]
Now you apply the theorem to your resulting vector:
\[
c = \sqrt{(-6)^2+4^2} \approx 7.21
\]

Answer 2

Don't hesitate to ask if you're not used to vector-geometry :)

Answer 3

if you have \[(x _{1},y _{1}) and (x _{2},y _{2})\]
the distance between them as follows
\[\sqrt{(x _{2}-x _{1})^{2}+(y _{2}-y _{1})^{2}}\]