Which points are 3 units away from 2 on the number line?
Answer and explanation
Correct answer: −1 and 5
The governing concept is distance on a number line. A point x is 3 units from 2 when |x − 2| = 3. This gives two possibilities: x − 2 = 3, so x = 5, or x − 2 = −3, so x = −1. Equivalently, move three units right from 2 to reach 5 and three units left to reach −1. Thus the two required points are −1 and 5. Option B gives points only one unit from 2, while option C includes −3, which is five units away, and option D gives distances 2 and 1. Therefore, option A is the only pair satisfying the distance condition.
Frequently asked questions
What is the correct answer to this question?
−1 and 5
Why is this the correct answer?
The governing concept is distance on a number line. A point x is 3 units from 2 when |x − 2| = 3. This gives two possibilities: x − 2 = 3, so x = 5, or x − 2 = −3, so x = −1. Equivalently, move three units right from 2 to reach 5 and three units left to reach −1. Thus the two required points are −1 and 5. Option B gives points only one unit from 2, while option C includes −3, which is five units away, and option D gives distances 2 and 1. Therefore, option A is the only pair satisfying the distance condition.
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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