A soccer player stands in the southeast corner of a 76-meter by 57-meter field and kicks a soccer ball all the way to a player in the opposite corner. That player kicks the ball down the length of the field to a player in the southwest corner. Finally, the player in the southwest
corner returns the ball back to the original player. How far has the ball traveled?

228m

Step-by-step explanation:

Let's draw a rectangle ABCD, A being its bottom left point, B bottom right, C top right and D top left.

That is our soccer field. The player stands in the southeast corner, which is top right corner or, in our case point B. He passes the ball to the player in the opposite corner, which is corner D. He then passes the ball to the player in the southwest corner, which is corner A. And he finally passes it back to the player in the corner B.

So, the ball goes from B to D to A to B. That means that the ball went along the circumference of the triangle DAB.

So, to answer how long the ball travelled we need to find the circumference of the triangle. The circumference is the sum of its three sides. One side is the field's length (76m) and the othet is field's width (57m). We only need to find the triangle's hypotenuse, side BD, using Pythagoras theorem:

BD² = AB² + AD²

BD² = 76² + 57²

BD = 95

So, the circumference of the triangle is 76+57+95=228m

answer: translate the circles so they share a common center point and dilate circle y by a scale factor of 3.