Question

Two football players are located at points AA and BB in a rectangular football field as shown at left. Point AA is located 5050 yards (\text{yd})(yd) from the west edge and 25 \, \text{yd}25yd from the south edge; Point BB is located 12 \, \text{yd}12yd from the east edge and 0 \, \text{yd}0yd from the south edge. What is the distance, in yards, between the two players? (Round your answer to the nearest tenth of a yard.)

Answer 1

45.5 yards.

Explanation:

We are given that two players are located at the points A and B in the rectangular field.

It is given that,

Point A is located 50 yards from the west edge and 25 yards from the south edge.

Thus, point A is given by the co-ordinate (50,25).

Also, Point B is located 12 yards from the east edge and 0 yards from the south edge.

So, point B is given by the co-ordinate (12,0).

Now, we need to find the distance between the points (50,25) and (12,0).

'The distance between two points
`(x_(1),y_(1))` and
`(x_(2),y_(2))` is given by
`\sqrt{(x_(2)-x_(1))^(2)+(y_(2)-y_(1))^(2)}`'.

So, the required distance is,

Distance between players =
`\sqrt{(12-50)^(2)+(0-25)^(2)}`

i.e. Distance between players =
`\sqrt{(-38)^(2)+(-25)^(2)}`

i.e. Distance between players =
`√(1444+625)`

i.e. Distance between players =
`√(2069)`

i.e. Distance between players = 45.5 yards.

Thus, the distance between the two players located at A and B is 45.5 yards.