Find the Distance Between Points D and K on a Number Line

Q: Why do we need absolute value for distance?

Distance is always positive! If you subtract in the wrong order, you might get a negative number. Using absolute value $ |a - b| $ guarantees your distance is positive, no matter which point you subtract first.

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

Yes! Counting is a great way to verify your answer. From D at -2 to K at 5, count each unit: that's 7 spaces total. This method works perfectly for checking your calculation.

Q: What if the points are both negative?

The same rule applies! For example, distance from -5 to -2 is $ |-2 - (-5)| = |3| = 3 $. Remember: distance is how far apart the points are, regardless of their signs.

Q: Does it matter which point I subtract first?

Not if you use absolute value! $ |5 - (-2)| = 7 $ and $ |(-2) - 5| = |-7| = 7 $ both give the same answer. The absolute value makes the order irrelevant.

Q: How do I handle decimal points on a number line?

The same way! If D was at -2.5 and K at 5.5, the distance would be $ |5.5 - (-2.5)| = |8| = 8 $ units. Always subtract coordinates and take absolute value.

Distance Calculations with Absolute Value

What is the distance between D and K?

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Understand the problem

What is the distance between D and K?

Step-by-step solution

We first mark the letter D on the number line and then proceed towards the letter K:

Note that the distance between the two letters is 7 steps.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Distance Formula: Use absolute value to find distance between points
Technique: Calculate |5 - (-2)| = |7| = 7 units
Check: Count spaces on number line: 7 spaces confirms answer ✓

Common Mistakes

Avoid these frequent errors

Forgetting to use absolute value for distance
Don't subtract D from K as 5 - (-2) = 7 without absolute value bars! This works here but fails when the first point is larger. Always use |point₂ - point₁| or count units to ensure positive distance.

Practice Quiz

Test your knowledge with interactive questions

$$ 5 < -5 $$

FAQ

Everything you need to know about this question

Why do we need absolute value for distance?

Distance is always positive! If you subtract in the wrong order, you might get a negative number. Using absolute value $|a - b|$ guarantees your distance is positive, no matter which point you subtract first.

Can I just count the spaces on the number line?

Yes! Counting is a great way to verify your answer. From D at -2 to K at 5, count each unit: that's 7 spaces total. This method works perfectly for checking your calculation.

What if the points are both negative?

The same rule applies! For example, distance from -5 to -2 is $|-2 - (-5)| = |3| = 3$ . Remember: distance is how far apart the points are, regardless of their signs.

Does it matter which point I subtract first?

Not if you use absolute value! $|5 - (-2)| = 7$ and $|(-2) - 5| = |-7| = 7$ both give the same answer. The absolute value makes the order irrelevant.

How do I handle decimal points on a number line?

The same way! If D was at -2.5 and K at 5.5, the distance would be $|5.5 - (-2.5)| = |8| = 8$ units. Always subtract coordinates and take absolute value.

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