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

1 Answer
Mar 17, 2016

Answer:

#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).