Based on the calculations, the measure of line HJ, JK, and HK are HJ = 25, JK = 25, and HK = 50.
How to determine the midpoint?
In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and divide by two (2).
Since J is the midpoint of line segment HK, it simply means that line segment HK is divided into two (2) sections HJ and JK and they are equal in length. By applying the midpoint rule, we have:
9x - 2 = 4x + 13
9x - 4x = 13 + 2
5x = 15
x = 15/5
x = 3.
For the measure of segment HJ, we have:
HJ = 9x - 2
HJ = 9(3) - 2
HJ = 27 - 2
HJ = 25 units.
For the measure of segment JK, we have:
JK = 4x + 13
JK = 4(3) + 13
JK = 12 + 13
JK = 25 units.
For the measure of segment HK, we have:
HK = HJ + JK
HK = 25 + 25
HK = 50 units.
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