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

1 Answer
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 = 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).