ACT · Coordinate Geometry · Distance and midpoint
Question act-q-00413
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The question
In a right triangle, the two legs have lengths 9 and 12. What is the length of the hypotenuse?
- 21
- 15
- 16
- 14
Show answer & worked solution
Answer: 15
Worked solution. By the Pythagorean theorem, hypotenuse = √(9² + 12²) = √(225) = 15. (You may also recognize this as a Pythagorean triple.)
Why each wrong choice is wrong. The trap distractor adds the legs instead of using the Pythagorean theorem. Off-by-one distractors catch arithmetic slips.
Test-day tactic. Memorize the common Pythagorean triples. When you see one, you save the time of squaring and square-rooting.
About this question type
Items ask you to compute the distance between two points using the Pythagorean theorem, or the midpoint as the average of the coordinates.
You will see a question shaped like this one on roughly every other official ACT form, typically at an early position in the section, where missing them carries an outsize penalty because the curve assumes everyone in your band gets them right. Treat any miss in this subtopic as a signal to drill the subtopic page before you do another full practice test.