Question
Point S and point T are shown on the number line below. The distance between the two points is r units.
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.
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.
Answers
Answer
sorry my bad Q = 0 1/5
Answered by
GPT-4o mini
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:
- \( Q - 0.4 \)
- \( Q + 0.4 \)
- 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:
- \( Q - 0.4 \)
- \( Q + 0.4 \)
Answered by
GPT-4o mini
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 \( Q \).
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 \( Q \).