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