On the number line, label the points that are 4 units away from 0.
If you fold the number line so that a vertical crease goes through 0, the points you label would match up. Explain why this happens.
To label the points that are 4 units away from 0 on the number line, we can start by drawing a number line with 0 in the middle. Then, we can count 4 units in each direction from 0 and label those points. The points labeled on the number line would be -4 and 4.
If you fold the number line so that a vertical crease goes through 0, the points you label (-4 and 4) would match up. This is because folding the number line along a vertical crease puts the positive and negative numbers on top of each other, aligning them perfectly. The crease acts as a mirror, reflecting the positive numbers on one side to match with the negative numbers on the other side. Therefore, the points labeled on the number line would overlap when folded, highlighting the symmetry of the number line about 0.
To label the points that are 4 units away from 0 on the number line, we need to find the points that are either 4 units to the right or 4 units to the left of 0.
Starting from 0, we can move 4 units to the right by adding 4: 0 + 4 = 4. So, 4 is one point that is 4 units away from 0 to the right.
Similarly, we can move 4 units to the left by subtracting 4: 0 - 4 = -4. So, -4 is another point that is 4 units away from 0 to the left.
Now, let's explore why these labeled points match up when the number line is folded along a vertical crease through 0.
When you fold the number line, you are essentially bringing the positive side of the number line closer to the negative side until they meet at 0, forming a straight line. This folding effectively reflects the points on the positive side to the negative side, creating symmetry.
Since 4 is labeled on the positive side of the number line, it would be reflected to the negative side and coincide with -4. This is because the distance between 0 and 4 is the same as the distance between 0 and -4, both being 4 units away.
Therefore, when you fold the number line along a vertical crease through 0, the points labeled as 4 units away from 0 on one side would match up with the points labeled as -4 units away on the other side due to the symmetry created by the folding.
I strongly suggest you actually do this with a piece of paper, like it
asked you to do.