Point S and point T are shown on the number line below. The distance between the two points is r units.

Question

S = 2 1/5 and T = 1 4/5

Point Q is shown on a second number line. Plot the points on the number line that are r units away from point Q.

Answer 1

To find the distance \( r \) between points \( S \) and \( T \), we first need to convert the mixed numbers into improper fractions or decimal form.

• Point \( S = 2 \frac{1}{5} = \frac{11}{5} = 2.2 \)
• Point \( T = 1 \frac{4}{5} = \frac{9}{5} = 1.8 \)

Now, we can find the distance \( r \):

\[ r = |S - T| = \left| \frac{11}{5} - \frac{9}{5} \right| = \left| \frac{2}{5} \right| = 0.4 \]

So, the distance \( r = 0.4 \) units.

Now, if we have a point \( Q \) on a second number line, we want to plot the points that are \( 0.4 \) units away from point \( Q \).

If we represent the position of point \( Q \) on the number line, the two points that are \( r = 0.4 \) units away from \( Q \) would be:

1. \( Q - 0.4 \)
2. \( Q + 0.4 \)

To plot these points, you would determine where \( Q \) is located, and then place markers at \( Q - 0.4 \) and \( Q + 0.4 \) on the number line.

If you provide a specific value for \( Q \), I could give exact coordinates. Otherwise, the points will be:

• \( Q - 0.4 \)
• \( Q + 0.4 \)

Answer 2

sorry my bad Q = 0 1/5

Answer 3

No problem! Let's find the points that are \( r = 0.4 \) units away from \( Q = 0 \frac{1}{5} \).

First, convert \( Q \) into an improper fraction or decimal:

• \( Q = 0 \frac{1}{5} = \frac{1}{5} = 0.2 \)

Now, we need to find the two points that are \( 0.4 \) units away from \( Q \):

1. Point 1: \[ Q - 0.4 = 0.2 - 0.4 = -0.2 \]

2. Point 2: \[ Q + 0.4 = 0.2 + 0.4 = 0.6 \]

Thus, the points that are \( 0.4 \) units away from \( Q \) are:

• \( -0.2 \)
• \( 0.6 \)

Plotting on the Number Line

On the number line, plot the following points:

• Mark \( Q = 0.2 \)
• Mark \( -0.2 \) to the left of \( 0 \)
• Mark \( 0.6 \) to the right of \( 0.2 \)

You would have:

• Point Q: \( 0.2 \)
• Point at \( Q - 0.4 \): \( -0.2 \)
• Point at \( Q + 0.4 \): \( 0.6 \)

These are the two points that are \( 0.4 \) units away from point \( Q \).