As shown in the figure, it is known that the numbers a, B and C corresponding to points a, B and C on the number axis are not 0, and C is the midpoint of ab. if [a + b] - [a-2c] + [b-2c] - [a + b-2c] =0, then the position of origin 0 is () A. On line AC, B. on line Ca, C. on line BC, D. on line CB Is the absolute value sign
If C is the midpoint of AB, then a + B = 2c, so
1,a+b-2c=0--->|a+b-2c|=0
2,a-2c=-b--->|a-2c|=|-b|=|b|
3,b-2c=-a--->|b-2c|=|-a|=|a|
Therefore, the original formula = | a + B | - | B | + | a | - 0 = 0
--->|a+b|=|b|-|a|
Because | a + B | > 0 --- > A, B is different sign, and | B | > | a |, is | ob | > | OA |, so the point O is between a and C