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: 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| $

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: 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.

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

$$ 5 < -5 $$

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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