Question

On a coordinate plane, a Ferris wheel is located at (12,5) and a roller coaster is located at (-5,5). What is the distance between the Ferris wheel and the roller coaster on the coordinate plane?

Answer 1

To find the distance between the Ferris wheel located at the point \( (12, 5) \) and the roller coaster located at the point \( (-5, 5) \), we can use the distance formula. However, since both points have the same \( y \)-coordinate, we can simply use the horizontal distance.

The distance between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) can be calculated using the formula:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

In this case, the coordinates are:
- \( (x_1, y_1) = (12, 5) \)
- \( (x_2, y_2) = (-5, 5) \)

Now, substituting the coordinates into the formula:

\[
d = \sqrt{((-5) - 12)^2 + (5 - 5)^2}
\]

Calculating the differences:

\[
= \sqrt{(-17)^2 + 0^2}
\]
\[
= \sqrt{289 + 0}
\]
\[
= \sqrt{289}
\]
\[
= 17
\]

Thus, the distance between the Ferris wheel and the roller coaster is \( \boxed{17} \).