Question

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

√(a - 25)^2

√(a - 5)^2

√a^2 + 5

√a^2 + 25

Explanation:

Step1: Recall the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).

Step2: Identify the coordinates

Here, \(x_1=a,y_1 = 0,x_2=0,y_2 = 5\).

Step3: Substitute into the formula

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

Answer:

\(\sqrt{a^{2}+25}\) (the fourth option)