Question

Which expression represents the distance between the points (a, 0) and (0, 5) on a coordinate grid?
StartRoot a squared + 5 EndRoot
StartRoot a squared + 25 EndRoot
StartRoot (a minus 25) squared EndRoot

Answer 1

To find the distance between the points \((a, 0)\) and \((0, 5)\) on a coordinate grid, we can use the distance formula, which is given by:

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

Substituting the coordinates of the points \((x_1, y_1) = (a, 0)\) and \((x_2, y_2) = (0, 5)\):

\[
d = \sqrt{(0 - a)^2 + (5 - 0)^2}
\]

This simplifies to:

\[
d = \sqrt{(-a)^2 + 5^2}
\]
\[
d = \sqrt{a^2 + 25}
\]

Therefore, the correct expression that represents the distance between the points \((a, 0)\) and \((0, 5)\) is:

\[
\sqrt{a^2 + 25}
\]

So the answer is:

\(\sqrt{a^2 + 25}\)