If A = 1.2, B = −3.8, and C = 4.2 on the number line, how much greater is distance AB than distance AC?
Answer and explanation
Correct answer: 2
The governing concept is that the distance between two points on a number line is the absolute value of their difference, because distance cannot be negative. Thus AB = |1.2 − (−3.8)| = |5.0| = 5 units. Similarly, AC = |1.2 − 4.2| = |−3.0| = 3 units. The question asks how much greater AB is than AC, so subtract the two distances: 5 − 3 = 2 units. Therefore, option A is correct. Option B gives only the smaller distance difference incorrectly, while options C and D do not follow from the calculated distances.
Frequently asked questions
What is the correct answer to this question?
2
Why is this the correct answer?
The governing concept is that the distance between two points on a number line is the absolute value of their difference, because distance cannot be negative. Thus AB = |1.2 − (−3.8)| = |5.0| = 5 units. Similarly, AC = |1.2 − 4.2| = |−3.0| = 3 units. The question asks how much greater AB is than AC, so subtract the two distances: 5 − 3 = 2 units. Therefore, option A is correct. Option B gives only the smaller distance difference incorrectly, while options C and D do not follow from the calculated distances.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Representing real numbers on the number line.
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