Mr. Kone Math Hub · Review sheet

Pythagorean Theorem and Distance

Unit 8: Pythagorean Theorem, Distance & Volume · NY-8.G.6, NY-8.G.7, NY-8.G.8

Grade 8 State Test

Notes

Which side is c?. c is always opposite the right angle — the longest side. Do not plug the hypotenuse in as a or b.

Distance formula is Pythagoras. From (x₁, y₁) to (x₂, y₂) the legs are |x₂ − x₁| and |y₂ − y₁|. So d = √((x₂ − x₁)² + (y₂ − y₁)²).

Vocabulary

  • hypotenuse: The side opposite the right angle in a right triangle.

Practice (no calculator unless marked)

  1. 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?
  2. Which list of numbers could represent the side lengths of a right triangle?
    • A. 5, 10, 13
    • B. 5, 12, 17
    • C. 10, 24, 26
    • D. 10, 24, 68
  3. 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?
    • A. 13
    • B. 15
    • C. √145
    • D. √185
  4. 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?
  5. Which list of numbers could represent the side lengths of a right triangle?
    • A. 5, 10, 13
    • B. 5, 12, 17
    • C. 10, 24, 26
    • D. 10, 24, 68
  6. 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?
    • A. 13
    • B. 15
    • C. √145
    • D. √185
  7. 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?
  8. Which list of numbers could represent the side lengths of a right triangle?
    • A. 5, 10, 13
    • B. 5, 12, 17
    • C. 10, 24, 26
    • D. 10, 24, 68