Question

Point M is the midpoint of JK, and JM = 18x - 3 meters and MK = 15x + 4 meters. Find the length (in meters) of JK.

a) 33x - 7 meters
b) 33x + 1 meters
c) 36x - 7 meters
d) 36x + 1 meters

Answer 1

By adding the lengths of the two segments JM and MK with M as the midpoint, we find that the length of JK is 33x + 1 meter.

Step-by-step explanation:

To find the length of line segment JK when given the lengths of the segments JM and MK with M as the midpoint, we add the two lengths together. Since M is the midpoint, JM and MK are two halves of the entire length of JK.

Given JM = 18x - 3 meters and MK = 15x + 4 meters, to find the full length of JK, we sum the lengths of JM and MK:

JK = JM + MK
JK = (18x - 3) + (15x + 4)
JK = 18x - 3 + 15x + 4
JK = (18x + 15x) + (-3 + 4)
JK = 33x + 1 meter

Therefore, the length of JK is 33x + 1 meter.