Aidan is participating in an 8 mile walk for his favorite charity. The organizers used a coordinate grid to plot the course. The starting point is at (3,1) and the ending point is at (3,9). At (3,7), there's a water station to make sure the walkers stay hydrated. How far along will Aidan be in the walk when he reaches the water station?

The distance that Aidan will be in the walk when he reaches the water station is; 2 miles

Formula for calculating distance between two coordinates is;

D = √[(y₂ - y₁)² + (x₂ - x₁)²]

Distance between starting point and endpoint is;

D = √[(9 - 1)² + (3 - 3)²]

D = √(8² + 0²)

D = 8 miles

Distance between starting point and water station is;

d = √[(7 - 1)² + (3 - 3)²]

d = √(6² + 0²)

d = 6 miles

Thus, the distance that Aidan will be in the walk when he reaches the water station is gotten from the difference between both distances.

Thus;

Distance of Aidan from water station = 8 - 6 = 2 miles

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Aidan is 2 miles far from the ending point when he reaches the water station.

Step-by-step explanation:

The locations of the starting point, water station and ending point are (3, 1), (3, 7) and (3, 9), all expressed in miles. First we determine the distances between starting and ending points and between starting point and water station by the Pythagorean Theorem:

From starting point to ending point:

(Eq. 1)

From starting point to water station:

(Eq. 2)

The distance between the water station and the ending point is:

(Eq. 3)

Hence, Aidan is 2 miles far from the ending point when he reaches the water station.