Answer: The distance between the points (3, 4) and (0, 0) is 5.
Step-by-step explanation: The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This theorem can be used to find the distance between two points in a coordinate system.
To find the distance between two points in a coordinate system, you can use the following steps:
Identify the coordinates of the two points.
Calculate the difference between the x-coordinates and the y-coordinates of the two points.
Use the Pythagorean Theorem to find the distance between the two points.
For example, to find the distance between the points (3, 4) and (0, 0), you would do the following:
Identify the coordinates of the two points: (3, 4) and (0, 0).
Calculate the difference between the x-coordinates and the y-coordinates of the two points: 3 - 0 = 3 for the x-coordinates and 4 - 0 = 4 for the y-coordinates.
Use the Pythagorean Theorem to find the distance between the two points: the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides, so the distance between the points is equal to the square root of 3^2 + 4^2 = 9 + 16 = 25 = 5.
Therefore, the distance between the points (3, 4) and (0, 0) is 5.