Finding Distance Between Points J and D on a Number Line: From 4 to -2

Q: Why is the distance 6 when J is at 4 and D is at -2?

Distance measures how far apart two points are, not their difference. From J at 4, you move left through 3, 2, 1, 0, -1, and finally reach D at -2. That's 6 steps total!

Q: Can distance ever be negative?

No! Distance is always positive because it represents length or space between points. Even when moving from positive to negative numbers, we count the total steps.

Q: What's the difference between distance and displacement?

Distance is always positive and measures total space traveled. Displacement considers direction and can be negative. For finding distance between points, we only care about the positive value.

Q: How do I remember the distance formula?

Think: Distance = |End - Start|. The absolute value bars ensure your answer is always positive, no matter which point you call 'start' or 'end'.

Q: Does it matter which point I start counting from?

No! Whether you count from J to D or D to J, the distance stays the same. Distance between two points is always equal regardless of direction.

Distance on Number Lines with Negative Numbers

What is the distance between J and D?

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Understand the problem

What is the distance between J and D?

Step-by-step solution

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

Note that the distance between the two letters is 6 steps

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Distance is always positive, regardless of direction on number line
Technique: Count steps from J at 4 to D at -2 = 6 units
Check: Use absolute value formula |4 - (-2)| = |6| = 6 ✓

Common Mistakes

Avoid these frequent errors

Subtracting coordinates without considering direction
Don't just calculate 4 - (-2) = 6 and think you're done! Students often forget that 4 to -2 means moving left through zero, which requires counting all steps. Always count each unit step or use the absolute value formula |x₁ - x₂|.

Practice Quiz

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$$ 5 < -5 $$

FAQ

Everything you need to know about this question

Why is the distance 6 when J is at 4 and D is at -2?

Distance measures how far apart two points are, not their difference. From J at 4, you move left through 3, 2, 1, 0, -1, and finally reach D at -2. That's 6 steps total!

Can distance ever be negative?

No! Distance is always positive because it represents length or space between points. Even when moving from positive to negative numbers, we count the total steps.

What's the difference between distance and displacement?

Distance is always positive and measures total space traveled. Displacement considers direction and can be negative. For finding distance between points, we only care about the positive value.

How do I remember the distance formula?

Think: Distance = |End - Start|. The absolute value bars ensure your answer is always positive, no matter which point you call 'start' or 'end'.

Does it matter which point I start counting from?

No! Whether you count from J to D or D to J, the distance stays the same. Distance between two points is always equal regardless of direction.

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