First solution:

Assign approximate values to every point. Let B=-1.3 (slightly less than -1), D=1.2 (slightly more than 1) and E=1.8 (slightly less than 2). Calculate the absolute value of every point, including assigned values: absolute value of point A is 2; of B is 1.3; of C is 0; of D is 1.2; of E is 1.7. Choose the maximum value, which is A.

Second solution:

Absolute value means symmetrical mapping relative to 0 for negative points while are positive points and 0 unchanged. Map points A and B symmetrically relative to 0 and choose the maximum value, which is A.

Third solution:

The absolute value of a number x is the distance between x and 0 on the number line. Thus only the end of the segment may be the right answer (point B has less absolute value than point A; point D has less absolute value than point E; point C is 0 so has the smallest absolute value). Point A is further from 0 than point E, so it is the right answer.

Strategy

Modeling the problem helps to understand it clearly.

Pitfalls:

Do not miss the word “absolute” (answer E is wrong).