Calculate the Distance Between Points F and B on a Number Line

Q: Why isn't the distance -4 since point B is at -4?

Distance and position are different! Position tells you where a point is located (can be negative), but distance tells you how far apart two points are (always positive).

Q: How do I calculate distance between any two points on a number line?

Use the formula: $ |x_2 - x_1| $. The absolute value bars ensure your answer is always positive, no matter which point you subtract from which.

Q: What if both points are negative numbers?

Same process! For example, distance from -2 to -5 is $ |-5 - (-2)| = |-3| = 3 $. The absolute value always makes the final answer positive.

Q: Can I just count the spaces on the number line?

Yes! Counting units between points works great for simple problems. From F (at 0) to B (at -4), count: 1, 2, 3, 4 units. This gives the same answer as the formula.

Distance on Number Lines with Negative Coordinates

What is the distance between F and B?

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What is the distance between F and B?

Step-by-step solution

One might think that as a consequence of the displacement on the axis being towards the negative domain, the result is also negative.

However it is important to keep in mind that here we are referring to the distance.

Distance can never be negative.

Even if the displacement is towards the negative domain, the distance is an existing value.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Distance Rule: Distance is always positive, never negative
Technique: Count units between points: F (0) to B (-4) = 4 units
Check: Use absolute value formula |0 - (-4)| = |4| = 4 ✓

Common Mistakes

Avoid these frequent errors

Thinking distance can be negative
Don't say the distance is -4 just because B is at -4! Distance measures how far apart points are, not their position direction. Always report distance as a positive number, even when moving toward negative values.

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FAQ

Everything you need to know about this question

Why isn't the distance -4 since point B is at -4?

Distance and position are different! Position tells you where a point is located (can be negative), but distance tells you how far apart two points are (always positive).

How do I calculate distance between any two points on a number line?

Use the formula: $|x_2 - x_1|$ . The absolute value bars ensure your answer is always positive, no matter which point you subtract from which.

What if both points are negative numbers?

Same process! For example, distance from -2 to -5 is $|-5 - (-2)| = |-3| = 3$ . The absolute value always makes the final answer positive.

Can I just count the spaces on the number line?

Yes! Counting units between points works great for simple problems. From F (at 0) to B (at -4), count: 1, 2, 3, 4 units. This gives the same answer as the formula.

Does it matter which point I start from?

No! Distance from F to B equals distance from B to F. Try both: $|0 - (-4)| = 4$ and $|(-4) - 0| = 4$ . Same result!

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