To determine the distance between the points [tex]\((3, 6)\)[/tex] and [tex]\((-3, 6)\)[/tex] on a coordinate plane, we use the distance formula.
The distance formula is given by:
[tex]\[
\text{distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\][/tex]
where [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] are the coordinates of the two points.
Let's apply this formula to our specific points:
1. Substitute the coordinates [tex]\((x_1, y_1) = (3, 6)\)[/tex] and [tex]\((x_2, y_2) = (-3, 6)\)[/tex] into the distance formula:
[tex]\[
\text{distance} = \sqrt{((-3) - 3)^2 + (6 - 6)^2}
\][/tex]
2. Simplify the expressions inside the square root:
[tex]\[
\text{distance} = \sqrt{(-3 - 3)^2 + (0)^2}
\][/tex]
[tex]\[
\text{distance} = \sqrt{(-6)^2 + 0}
\][/tex]
[tex]\[
\text{distance} = \sqrt{36}
\][/tex]
3. Finally, take the square root of 36 to find the distance:
[tex]\[
\text{distance} = 6
\][/tex]
Hence, the distance between the points [tex]\((3, 6)\)[/tex] and [tex]\((-3, 6)\)[/tex] is [tex]\(6.0\)[/tex].
