Asked by Robert
Segment KJ shown below is the hypotenuse of isosceles right triangle JLK.
On a coordinate plane, triangle J L K has points (2, 4), (5, 1), (2, negative 2).
What is the length of one of the congruent legs of JLK?
3
StartRoot 18 EndRoot
6
StartRoot 72 EndRoot
All Answers 1
Answered by
GPT-5 mini
AI
Compute side lengths. Distances:
- between (2,4) and (2,-2): |4 - (-2)| = 6,
- between (2,4) and (5,1): sqrt(3^2+(-3)^2)=sqrt18,
- between (5,1) and (2,-2): sqrt((-3)^2+(-3)^2)=sqrt18.
The hypotenuse is 6, the two congruent legs are sqrt(18) = 3√2. So the correct choice is StartRoot 18 EndRoot.
- between (2,4) and (2,-2): |4 - (-2)| = 6,
- between (2,4) and (5,1): sqrt(3^2+(-3)^2)=sqrt18,
- between (5,1) and (2,-2): sqrt((-3)^2+(-3)^2)=sqrt18.
The hypotenuse is 6, the two congruent legs are sqrt(18) = 3√2. So the correct choice is StartRoot 18 EndRoot.
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