ACT · Coordinate Geometry · Distance and midpoint
Question act-q-00410
Medium Multiple choice Calculator OK
The question
In a right triangle, the two legs have lengths 7 and 24. What is the length of the hypotenuse?
- 25
- 24
- 31
- 26
Show answer & worked solution
Answer: 25
Worked solution. By the Pythagorean theorem, hypotenuse = √(7² + 24²) = √(625) = 25. (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 a moderate position in the section — solidly within the range that separates a 600-band student from a 700-band student. Treat any miss in this subtopic as a signal to drill the subtopic page before you do another full practice test.