Answer
$\sqrt{5y^2-2xy+x^2} \text{ units}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the Distance Formula to find the distance between the given points $\left(
x+y,y
\right)$ and $\left(
x-y,x
\right)$.
$\bf{\text{Solution Details:}}$
With the given points, then $x_1=
x+y
,$ $x_2=
x-y
,$ $y_1=
y
,$ and $y_2=
x
.$ Using the Distance Formula which is given by $d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}
,$ then
\begin{array}{l}\require{cancel}
d=\sqrt{(x+y-(x-y))^2+(y-x)^2}
\\\\
d=\sqrt{(x+y-x+y)^2+(y-x)^2}
\\\\
d=\sqrt{(2y)^2+(y-x)^2}
\\\\
d=\sqrt{4y^2+(y-x)^2}
.\end{array}
Using the square of a binomial which is given by $(a+b)^2=a^2+2ab+b^2$ or by $(a-b)^2=a^2-2ab+b^2,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
d=\sqrt{4y^2+y^2-2xy+x^2}
\\\\=
d=\sqrt{5y^2-2xy+x^2}
.\end{array}
Hence, the distance is $
\sqrt{5y^2-2xy+x^2} \text{ units}
.$
