Final answer:
To find the length of KL in the given square, we can use the distance formula and the coordinates of the vertices. The calculation gives us a length of approximately 4 units.
Step-by-step explanation:
To find the length of KL, we can use the distance formula. The distance formula is based on the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, KL is a side of the square, so it is equal in length to the other sides. The distance formula between two points (x1, y1) and (x2, y2) is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using the given coordinates: J(2,-1), K(-1,-4), L(-4,-1), and M(-1, 2), we find:
d(KL) = sqrt((-1 - (-4))^2 + (-4 - (-1))^2) = sqrt(3^2 + (-3)^2) = sqrt(9 + 9) = sqrt(18)
Rounding to the nearest whole number, the length of KL is approximately 4 units.