Question

How do you use the Pythagorean theorem to find the distance between the points (3,0) and (-3,6)?

Answer 1

`6^2 + 6^2 = c^2; 72 = c^2; c = sqrt72 = 8.48528`

Explanation:

To use the Pythagorean theorem to find the distance between (3, 0) and (-3, 6) we must form a right triangle. The horizontal distance is 6 (the distance from -3 to 3 on the `x` axis). The vertical distance is also 6 (the distance from `y = 6` to `y = 0`), and the angle is a right angle. The Pythagorean theorem states that the squares of both sides added together is equal to the hypotenuse squared (`a^2 + b^2 = c^2`). Therefore:

`6^2 + 6^2 = c^2` and `c` in this case is the distance between (3, 0) and (-3, 6).

`6^2 + 6^2 = 36 + 36 = 72 = c^2`, so `c = sqrt72 = 8.48528`

Rounding this to the hundredths would give `c = 8.49`. This is the distance between the points (3, 0) and (-3, 6).