Find the Distance Between Points I and E on a Number Line

Q: Why do I need to use absolute value when subtracting?

Distance is always positive! If you subtract in the wrong order, you might get a negative number. The absolute value ensures your distance is always positive, no matter which point you subtract from first.

Q: Can I just count the spaces between the points?

Yes! Counting units is a great visual method. Just be careful to count the spaces between tick marks, not the tick marks themselves. From -1 to 3, you move through 0, 1, and 2, which is 4 spaces total.

Q: What if both points are negative numbers?

The same rule applies! For example, from -5 to -2: $ |-2 - (-5)| = |3| = 3 $. You can also count: -5→-4→-3→-2 = 3 units.

Q: Does the order of subtraction matter?

Not when you use absolute value! $ |3 - (-1)| = 4 $ gives the same result as $ |(-1) - 3| = 4 $. The absolute value makes both calculations equal.

Q: How is this different from adding the numbers?

Distance measures space between points, not their sum! Think of it like measuring the length of a rope stretched between two pegs - you don't add the peg positions, you measure the rope length.

Distance Calculation with Integer Coordinates

What is the distance between I and E?

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Understand the problem

What is the distance between I and E?

Step-by-step solution

We first mark the letter I on the number line and then proceed towards the letter E:

Note that the distance between the two letters is 4 steps.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Distance Formula: Count units between two points on number line
Technique: From -1 to 3 count: -1→0→1→2→3 = 4 units
Check: Subtract coordinates: |3 - (-1)| = |4| = 4 ✓

Common Mistakes

Avoid these frequent errors

Adding coordinates instead of finding absolute difference
Don't add the coordinates like 3 + (-1) = 2! This gives the wrong distance because you're not measuring the space between points. Always subtract coordinates and take absolute value: |3 - (-1)| = 4.

Practice Quiz

Test your knowledge with interactive questions

$$ 5 < -5 $$

FAQ

Everything you need to know about this question

Why do I need to use absolute value when subtracting?

Distance is always positive! If you subtract in the wrong order, you might get a negative number. The absolute value ensures your distance is always positive, no matter which point you subtract from first.

Can I just count the spaces between the points?

Yes! Counting units is a great visual method. Just be careful to count the spaces between tick marks, not the tick marks themselves. From -1 to 3, you move through 0, 1, and 2, which is 4 spaces total.

What if both points are negative numbers?

The same rule applies! For example, from -5 to -2: $|-2 - (-5)| = |3| = 3$ . You can also count: -5→-4→-3→-2 = 3 units.

Does the order of subtraction matter?

Not when you use absolute value! $|3 - (-1)| = 4$ gives the same result as $|(-1) - 3| = 4$ . The absolute value makes both calculations equal.

How is this different from adding the numbers?

Distance measures space between points, not their sum! Think of it like measuring the length of a rope stretched between two pegs - you don't add the peg positions, you measure the rope length.

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