Final answer:
Segments JK and LM are congruent with each having a length of 5 units, derived using the distance formula.
Step-by-step explanation:
To determine whether segments JK and LM are congruent, we calculate the lengths using the distance formula which is √((x2-x1)² + (y2-y1)²). For segment JK, we have J(1,4) and K(5,1), so the length is √((5-1)² + (1-4)²) = √(16 + 9) = √25 = 5 units. For segment LM, we have L(3,5) and M(0,9), so the length is √((0-3)² + (9-5)²) = √(9 + 16) = √25 = 5 units. Since the lengths are both equal to 5 units, segments JK and LM are congruent.