To find the distance between the points \( (3, 0) \) and \( (0, 4) \) using the Pythagorean theorem, you can treat the distance as the hypotenuse of a right triangle formed by the x and y differences of the points.
-
Find the differences in the x-coordinates and y-coordinates:
- \( \Delta x = x_2 - x_1 = 0 - 3 = -3 \)
- \( \Delta y = y_2 - y_1 = 4 - 0 = 4 \)
-
Use the Pythagorean theorem: \[ d = \sqrt{(\Delta x)^2 + (\Delta y)^2} \] Substituting the values: \[ d = \sqrt{(-3)^2 + (4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \]
Therefore, the distance between the points \( (3, 0) \) and \( (0, 4) \) is 5 feet.
3 answers