Question

which expression represents the distance between point $(0,a)$ and point $(a,0)$ on a coordinate grid? 0 $sqrt{2a^{4}}$ $sqrt{a^{4}}$ $sqrt{2a^{2}}$

Explanation:

Step1: Recall the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here, \(x_1 = 0,y_1=a,x_2=a,y_2 = 0\).

Step2: Substitute the values into the formula

Substitute the values into the formula: \(d=\sqrt{(a - 0)^2+(0 - a)^2}=\sqrt{a^{2}+(-a)^{2}}\).

Step3: Simplify the expression

Since \((-a)^{2}=a^{2}\), then \(d=\sqrt{a^{2}+a^{2}}=\sqrt{2a^{2}}\).

Answer:

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