courses › Geometry

Right triangles, distances, and midpoints.

Pen and paper is fine · no calculator needed why?

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Opens at level 23.

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Builds on: Exponents & roots (not open yet)

skills · practice stats

From rounds of this course only: box, review and trial answers are left out. Once a skill has 40 tries, it compares your first 20 tries with your last 20.

• Hypotenuse par 14 s not tried yet

  worked example

  A right triangle has legs 42 and 40. How long is the hypotenuse?

  Answer: 58

  1. √(42² + 40²) = √(1,764 + 1,600) = √3,364 = 58.
  2. It is the 20-21-29 triangle scaled by 2.

• Midpoint par 14 s not tried yet

  worked example

  What is the midpoint of (−5, −4) and (−1, −8)? Enter x, y.

  Answer: (-3, -6)

  1. Average each coordinate: (−5 + (−1)) ÷ 2 = −3 and (−4 + (−8)) ÷ 2 = −6.
  2. The midpoint is (−3, −6).

• Missing leg par 17 s not tried yet

  worked example

  A right triangle has hypotenuse 51 and one leg 24. How long is the other leg?

  Answer: 45

  1. √(51² − 24²) = √(2,601 − 576) = √2,025 = 45.

• Distance between points par 20 s not tried yet

  worked example

  What is the distance between (3, −8) and (12, 4)?

  Answer: 15

  1. The x-values differ by 9 and the y-values by 12.
  2. Distance = √(9² + 12²) = √(81 + 144) = √225 = 15.

rest ladder

Win 3 of your last 4 rounds and the course rests. A win is 90% right, within 2× the round's par. Pass the review when it comes back and the next rest is longer.

1. 1 day
2. 3 days
3. 7 days
4. 14 days
5. 30 days
6. 60 days
7. mastered · every 90 days

your rounds

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