Question

which expression represents the distance between the points \\((a, 0)\\) and \\((0, 5)\\) on a coordinate grid?

• \\(\sqrt{a^2 + 5}\\)
• \\(\sqrt{a^2 + 25}\\)
• \\(\sqrt{(a - 25)^2}\\)
• \\(\sqrt{(a - 5)^2}\\)

Explanation:

Identify the given coordinates

$$ (x_1, y_1) = (a, 0),\quad (x_2, y_2) = (0, 5) $$

Apply the distance formula

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

Substitute and simplify

$$ d = \sqrt{(0 - a)^2 + (5 - 0)^2} = \sqrt{(-a)^2 + 5^2} = \sqrt{a^2 + 25} $$

Answer:

• (A) \(\sqrt{a^2 + 5}\)
• (B) \(\sqrt{a^2 + 25}\) (Correct answer)
• (C) \(\sqrt{(a - 25)^2}\)
• (D) \(\sqrt{(a - 5)^2}\)