To determine the distance between points [tex]\( A \)[/tex] and [tex]\( B \)[/tex] on a coordinate plane, we use the distance formula. The distance formula for two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[
\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\][/tex]
In this specific problem, the points [tex]\( A \)[/tex] and [tex]\( B \)[/tex] have coordinates [tex]\( A(0, 0) \)[/tex] and [tex]\( B(a, 0) \)[/tex], respectively.
1. Identify the coordinates:
- [tex]\( A(0, 0) \)[/tex]
- [tex]\( B(a, 0) \)[/tex]
2. Substitute the coordinates into the distance formula:
[tex]\[
\sqrt{(a - 0)^2 + (0 - 0)^2}
\][/tex]
3. Simplify the expression inside the square root:
[tex]\[
\sqrt{a^2 + 0}
\][/tex]
[tex]\[
\sqrt{a^2}
\][/tex]
4. Simplify further:
[tex]\[
a
\][/tex]
The distance from point [tex]\( A \)[/tex] to point [tex]\( B \)[/tex] is [tex]\( a \)[/tex].
Review the provided options:
A. [tex]\((a-a)^2+(b-b)^2=a^2\)[/tex]
B. [tex]\(\sqrt{(a-0)^2+(0-0)^2}=\sqrt{a^2}=a\)[/tex]
C. [tex]\((a-0)^2+(0-0)^2=a^2\)[/tex]
D. [tex]\(\sqrt{(a-0)^2+(b-b)^2}=\sqrt{a^2}=a\)[/tex]
The correct formula and steps are reflected in option B:
[tex]\[
\sqrt{(a-0)^2+(0-0)^2}=\sqrt{a^2}=a
\][/tex]
Thus, the answer is [tex]\( \boxed{B} \)[/tex].
