Finding Distance Between Points D and I on a Number Line

Q: Why is the distance between -2 and 3 equal to 5?

Distance is always positive and measures how far apart two points are. From -2 to 3, you move 5 units: 2 units to get to 0, then 3 more units to reach 3.

Q: Does it matter which point I subtract from which?

No! You can use either $ |3 - (-2)| $ or $ |(-2) - 3| $. Both give the same answer: 5. The absolute value ensures the result is always positive.

Q: Can I use this method for any two points on a number line?

Yes! The distance formula $ |x_2 - x_1| $ works for any two points, whether they're both positive, both negative, or mixed like in this problem.

Distance Calculation with Negative and Positive Numbers

What is the distance between D and I?

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Understand the problem

What is the distance between D and I?

Step-by-step solution

Let's begin by marking the letter D on the number line and then proceeding towards the letter I:

Note that the distance between the two letters is 5 steps

Final Answer

Key Points to Remember

Essential concepts to master this topic

Distance Formula: Always use absolute value of the difference between coordinates
Technique: From D at -2 to I at 3: |3 - (-2)| = |5| = 5
Check: Count steps on number line: -2 → -1 → 0 → 1 → 2 → 3 = 5 steps ✓

Common Mistakes

Avoid these frequent errors

Forgetting to use absolute value with negative numbers
Don't just subtract 3 - (-2) = 5 without absolute value bars when dealing with mixed positive/negative coordinates = wrong understanding! Students often get confused with direction. Always use |final position - starting position| to ensure distance is positive.

Practice Quiz

Test your knowledge with interactive questions

All negative numbers appear on the number line to the left of the number 0.

FAQ

Everything you need to know about this question

Why is the distance between -2 and 3 equal to 5?

Distance is always positive and measures how far apart two points are. From -2 to 3, you move 5 units: 2 units to get to 0, then 3 more units to reach 3.

What if I get a negative answer when calculating distance?

Distance can never be negative! If you get a negative result, you forgot the absolute value. Remember: distance = $|x_2 - x_1|$

Does it matter which point I subtract from which?

No! You can use either $|3 - (-2)|$ or $|(-2) - 3|$ . Both give the same answer: 5. The absolute value ensures the result is always positive.

How do I count steps on a number line correctly?

Start at the first point and count each unit you move to reach the second point. From D(-2): count -2 → -1 → 0 → 1 → 2 → 3. That's 5 steps total.

Can I use this method for any two points on a number line?

Yes! The distance formula $|x_2 - x_1|$ works for any two points, whether they're both positive, both negative, or mixed like in this problem.

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