Question

On rectangle DEFG, it D is located at (-1 -1) and F is located at (4 -8), what is the length of GE

Answer 1

First we have to notice that the lenght GE is the same as the length DF, this comes from the fact that the diagonals in any rectangle have the same length. Now that we know that we have to remember that the distance between two points is given as:

`d(A,B)=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}`

In this case we have that:

`\begin{gathered} d(G,E)=d(D,F)=\sqrt[]{(4-(-1))^2+(-8-(-1))^2} \\ =\sqrt[]{(5)^2+(-7)^2} \\ =\sqrt[]{25+49} \\ =\sqrt[]{74} \end{gathered}`

Therefore the distance between GE is

`\sqrt[]{74}`

this is appoximately 8.602