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

Mar 17, 2016

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 $c = \sqrt{72} = 8.48528$

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