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

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

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Answer 1 · 2016-03-17T07:13:04

$6^{2} + 6^{2} = c^{2}; 72 = c^{2}; c = \sqrt{72} = 8.48528$ $6^2 + 6^2 = c^2; 72 = c^2; c = sqrt72 = 8.48528$

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 $x$ $x$ axis). The vertical distance is also 6 (the distance from $y = 6$ $y = 6$ to $y = 0$ $y = 0$ ), 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 ( $a^{2} + b^{2} = c^{2}$ $a^2 + b^2 = c^2$ ). Therefore:

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

$6^{2} + 6^{2} = 36 + 36 = 72 = c^{2}$ $6^2 + 6^2 = 36 + 36 = 72 = c^2$ , so $c = \sqrt{72} = 8.48528$ $c = sqrt72 = 8.48528$

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

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

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