Question

what is the length of the segment connecting points (1,2) and (5,5) in the xy-coordinate plane

Answer 1

5

Answer 2

it is a right triangle, and its a 3-4-5 triangle at that. The five is the hypotenuse

Answer 3

\[d(P_{1},P_{2})=\sqrt{(x _{1}-x _{2})^{2}+(y _{1}-y _{2})^{2}}\]
\[d((1,2),(5,5))=\sqrt{(1 -5 )^{2}+(2 -5)^{2}}\]
\[d((1,2),(5,5))=\sqrt{(-4)^{2}+(-3)^{2}}\]
\[d((1,2),(5,5))=\sqrt{16+9}\]
\[d((1,2),(5,5))=\sqrt{25}\]
\[d((1,2),(5,5))=5\]