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√2

Step-by-step explanation:

The congruent length of the triangle are the lengths with equal lengths. For an isosceles triangle, two of its sides are equal. In order to know the length of one of the congruent legs of JLK, we will find the distance between the adjacent point of the triangle.

Given triangle J L K has points J(2, 4), K(5, 1) andL (2, -2).

Using the formula to calculating distance between two points

D = √(x2-x1)²+(y2-y1)²

For side JK,

J(2, 4), K(5, 1)

JK = √(5-2)²+(1-4)²

JK = √3²+-3²

JK = √18

JK = 3√2

For side KL,

K(5,1), L(2, -2)

KL = √(2-5)²+(-2-1)²

KL = √-3²+-3²

KL = √18

KL = 3√2

For side JL

J(2, 4), L(2, -2)

JL= √(2-2)²+(-2-4)²

JL = √0²+-6²

JL = √36

JL = 6

SINCE JK = KL = 3√2, the length of one of the congruent legs is 3√2

$32,660

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