The expression below represents the distance between two points on a number line:

Question

∣ -5−3 | Show on the number line the two points?

Answer 1

To find the distance between the two points represented by the expression \(|-5 - 3|\), we start by calculating it.

1. Evaluate the expression inside the absolute value: \(-5 - 3 = -8\)

2. Take the absolute value: \(|-8| = 8\)

This means the distance between the two points is 8 units.

Now, let's identify the two points based on this expression. The expression can also be interpreted in terms of coordinates. It looks like we are considering the points \(-5\) and \(-3\).

On a number line:

• The point \(-5\) is located to the left of \(-3\).
• The point \(-3\) is located to the right of \(-5\).

So, on the number line, you would represent:

• One point at \(-5\)
• The other point at \(-3\)

The distance between \(-5\) and \(-3\) is indeed 8 units; however, note that the points need to be defined clearly based on the interpretation. If we were looking for only the numbers \(-5\) and \(-3\), the distance calculated using \(|x_1 - x_2|\) where \(x_1 = -5\) and \(x_2 = -3\) results in \( | -5 - (-3) | = | -5 + 3 | = | -2 | = 2\).

So, the points shown with correct distance being considered would be \(-5\) and \(-3\) marked on the number line and the distance between them is 2.

The visual representation on the number line looks like this:

<----|----|----|----|----|----|----|----|---->
    -8   -7   -6    -5   -4   -3   -2   -1   0

Mark the points:

• \(-5\) and \(-3\) would be highlighted.