Unit 8 · Pythagorean Theorem, Distance & Volume
In a right triangle, a² + b² = c², where c is the hypotenuse. Distance on the plane is the hypotenuse of a slope triangle.
c is always opposite the right angle — the longest side. Do not plug the hypotenuse in as a or b.
From (x₁, y₁) to (x₂, y₂) the legs are |x₂ − x₁| and |y₂ − y₁|. So d = √((x₂ − x₁)² + (y₂ − y₁)²).
The side opposite the right angle in a right triangle.
Example: If legs are 3 and 4, the hypotenuse is 5.
Try the prompt first. The steps stay folded until you ask to see them.
A park path runs from (1, 2) to (5, 5) on a coordinate grid where 1 unit = 20 meters. How long is the path?
Watch for
Adding the legs instead of using squares
The relationship is among areas of squares on the sides, not the lengths themselves.
Fix: Sketch the three squares.
Submit each answer to check it. The key is not shown until you do.
Triangle DEF is a right triangle with a right angle at vertex F. Side DF has a length of 9 inches and side FE has a length of 12 inches. What is the length, in inches, of side DE?
Which list of numbers could represent the side lengths of a right triangle?
Two points are plotted on a coordinate plane. Point A is plotted at (−11, 8) and point B is plotted at (−2, −4). What is the distance, in units, from point A to point B?
Always label legs and hypotenuse on a sketch before substituting.
Determine whether 9, 12, 15 is a right triangle by testing a² + b² = c².
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