The length of segment AB is 37 cm. Point C and M lie on the same segment, and point m is between points B and C.

| July 24, 2021 | education

The length of segment AB is 37 cm. Point C and M lie on the same segment, and point m is between points B and C. Find the length of the segment CM if a) AC = 12cm MB = 17cm b) AM = 26cm CB = 18cm

By the condition of the problem, we know that points C and M lie on the segment AB, and the point M is between B and C. We got that the segment AB is divided by the segments AC, CM and MB.

AB = AC + CM + MB.

a) AB = 37; AC = 12; MB = 17. Substitute in the equation:

CM = AB – AC – MB = 37 – 12 – 17 = 8.

b) AB = 37; AM = 26; СB = 18.

AB = AC + CB;

AC = AB – CB = 37 – 18 = 19.

AB = MB + AM;

MВ = AB – AM = 37 – 26 = 11.

Now we know AC and M. Substitute in the equation:

CM = AB – AC – MB = 37 – 19 – 11 = 7.

Answer: a) the length of the segment CM = 8; b) the length of the segment CM = 7.



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