The following coordinates represent the location of different events at an upcoming track meet. Based on the coordinate plane, how far is the pole vault from the long jump?

(1 point)
Responses

2.5 units
2.5 units

7 units
7 units

4 units
4 units

3 units

Given:
High jump: (2,5)
Pole Vault (5,5)
Long jump (5,2)
Hurdle (1,2)

1 answer

To find the distance between the Pole Vault and the Long Jump, we can use the distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\):

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

The coordinates for the Pole Vault are \((5,5)\) and for the Long Jump are \((5,2)\). Plugging in these coordinates:

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

Calculating this gives:

\[ d = \sqrt{(0)^2 + (-3)^2} \] \[ d = \sqrt{0 + 9} \] \[ d = \sqrt{9} \] \[ d = 3 \]

Therefore, the distance between the Pole Vault and the Long Jump is 3 units.