3. What is the perimeter of the entire playing surface? *Do not count the inside lines.* Show your work to receive credit. Answers should be in simplest radical form. (2 points)
You and your friend are standing diagonally across from one another on the four-square court. You are throwing the ball back and forth, waiting for two other people to join you, so you can begin the game. You are standing at the coordinate (-3, 7) and your friend is standing at the coordinate (7, -3).
Each side of the square is 2square root 3, since the length of one side is 2 square root 3
The perimeter is then 4 times the length of one side which is 4 x 2square root 3= 8 square root 3
So the perimeter of the entire playing surface is 8 square root 3
4. How far are you throwing the ball? Show your work to receive credit. Answers should be in simplest radical form. (2 points)
To find the distance between two points (-3, 7) and (7, -3), we can use the distance formula.
The distance formula is √((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the coordinates into the formula, we get:
√((7 - (-3))^2 + (-3 - 7)^2)
= √((10)^2 + (-10)^2)
= √(100 + 100)
= √200
= 10√2
So, you are throwing the ball a distance of 10√2.
To find the distance between the coordinates (-3, 7) and (7, -3), we can use the distance formula.
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the values, we get:
Distance = √((7 - (-3))^2 + (-3 - 7)^2)
= √((7 + 3)^2 + (-3 - 7)^2)
= √(10^2 + (-10)^2)
= √(100 + 100)
= √200
= √(2 * 100)
= √2 * √100
= 10√2
So you are throwing the ball a distance of 10√2.
To find the distance you are throwing the ball, you can use the distance formula. The distance formula is given by the equation:
d = √((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) represents your coordinates and (x2, y2) represents your friend's coordinates.
In this case, your coordinates are (-3, 7) and your friend's coordinates are (7, -3). Plugging these values into the distance formula, we get:
d = √((7 - (-3))^2 + (-3 - 7)^2)
= √((7 + 3)^2 + (-3 - 7)^2)
= √(10^2 + (-10)^2)
= √(100 + 100)
= √200
To simplify the radical, we can factor out the largest square number that divides evenly into 200, which is 4:
√200 = √(4 * 50)
= √4 * √50
= 2√50
So the distance you are throwing the ball is 2√50.