Which points are 4 units away from −2 on the number line?
Answer and explanation
Correct answer: −6 and 2
The governing concept is absolute distance on a number line. A point x is 4 units from −2 when |x − (−2)| = 4, or |x + 2| = 4. Solving the two cases gives x + 2 = 4, hence x = 2, and x + 2 = −4, hence x = −6. Thus the points are −6 and 2, one lying four units to the left and the other four units to the right of −2. Option B gives distances 2 and 6; option C includes the starting point itself; and option D gives distances 2 and 8. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
−6 and 2
Why is this the correct answer?
The governing concept is absolute distance on a number line. A point x is 4 units from −2 when |x − (−2)| = 4, or |x + 2| = 4. Solving the two cases gives x + 2 = 4, hence x = 2, and x + 2 = −4, hence x = −6. Thus the points are −6 and 2, one lying four units to the left and the other four units to the right of −2. Option B gives distances 2 and 6; option C includes the starting point itself; and option D gives distances 2 and 8. Therefore, option A is correct.
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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