If (A=2.4), (B=-1.8), and (C=5.1), what is the difference between lengths (AB) and (AC)?

Correct answer: (1.5)

The direct answer is option A, 1.5. A length on the number line is found by taking the absolute difference of the endpoint coordinates. For AB, use \(AB=|A-B|=|2.4-(-1.8)|=|2.4+1.8|=4.2\). For AC, use \(AC=|A-C|=|2.4-5.1|=|-2.7|=2.7\). The difference between the lengths is \(|4.2-2.7|=1.5\). Option A is therefore correct. Option B, 2.7, is only the length AC, not the difference between AB and AC. Option C, 4.2, is only the length AB, not the requested difference. Option D, 6.9, comes from adding the two lengths, \(4.2+2.7\), whereas the question asks for their difference. Absolute value is important because a length cannot be negative. The points' order does not matter when calculating distance. Memory cue: first calculate both lengths with absolute values, then subtract the two lengths and take the positive result.