find the distance between point A(5,3) and point B (1,0) on a graph using the Pythagorean Theorem.
To find the distance between two points using the Pythagorean Theorem, you need to determine the difference in the x-coordinates and the y-coordinates of the two points. Here's how you can calculate the distance between point A(5,3) and point B(1,0):
Step 1: Determine the difference in x-coordinates
- Subtract the x-coordinate of Point B from the x-coordinate of Point A: 5 - 1 = 4
Step 2: Determine the difference in y-coordinates
- Subtract the y-coordinate of Point B from the y-coordinate of Point A: 3 - 0 = 3
Step 3: Apply the Pythagorean Theorem
- 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 other two sides.
- In this case, the horizontal difference (4) represents one side of the right triangle (one "leg") and the vertical difference (3) represents the other side.
- The distance between the two points is the length of the hypotenuse, which we can calculate using the Pythagorean Theorem.
c^2 = a^2 + b^2
Substituting the values into the formula:
c^2 = 4^2 + 3^2
c^2 = 16 + 9
c^2 = 25
Taking the square root of both sides:
c = √25
c = 5
Therefore, the distance between point A(5,3) and point B(1,0) is 5 units.