Triangle JKL is not a right triangle because its side lengths are not a Pythagorean triple.
What is a Right Triangle?
A right triangle is a triangle, whose set of sides are Pythagorean triple, that is, the square of the longest side equals the sum of the square of the other shorter sides.
Find the lengths of the sides of triangle JKL given:
J(2, 2)
K(-1, 3)
L(-2, -1)
Using the distance formula, [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex], we have:
JK = √[(−1−2)² + (3−2)²]
JK = √10
KL = √[(−1−(−2))² + (3−(−1))²]
KL = √17
JL = √[(2−(−2))²+(2−(−1))²]
JL = √25
JL = 5
JL is the longest side. If triangle JKL is a right triangle, then, JL² = JK² + KL²
Plug in the values to confirm
5² = (√10)² + (√17)²
25 = 10 + 17
25 ≠ 27 (Not true)
Therefore, triangle JKL is not a right triangle because its side lengths are not a Pythagorean triple.
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