Question
Find the midpoint of segment AB. A is, (2,4) and B is, (8,6)
Answers
Answered by
GPT-4o mini
The midpoint \( M \) of a segment with endpoints \( A(x_1, y_1) \) and \( B(x_2, y_2) \) can be found using the formula:
\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
For the given points \( A(2, 4) \) and \( B(8, 6) \):
- \( x_1 = 2 \)
- \( y_1 = 4 \)
- \( x_2 = 8 \)
- \( y_2 = 6 \)
Now, we can plug these values into the formula:
\[
M = \left( \frac{2 + 8}{2}, \frac{4 + 6}{2} \right)
\]
\[
M = \left( \frac{10}{2}, \frac{10}{2} \right)
\]
\[
M = (5, 5)
\]
The midpoint of segment AB is \( (5, 5) \).
\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
For the given points \( A(2, 4) \) and \( B(8, 6) \):
- \( x_1 = 2 \)
- \( y_1 = 4 \)
- \( x_2 = 8 \)
- \( y_2 = 6 \)
Now, we can plug these values into the formula:
\[
M = \left( \frac{2 + 8}{2}, \frac{4 + 6}{2} \right)
\]
\[
M = \left( \frac{10}{2}, \frac{10}{2} \right)
\]
\[
M = (5, 5)
\]
The midpoint of segment AB is \( (5, 5) \).
Answer
Please use better typing to explain how you got it. I can't understand it.
Answered by
GPT-4o mini
Sure! Let's break it down step by step in a clearer way.
To find the **midpoint** of a line segment connecting two points \( A \) and \( B \), we use a specific formula. The points given are:
- Point \( A \) has coordinates \( (2, 4) \).
- Point \( B \) has coordinates \( (8, 6) \).
### Step 1: Identify the Coordinates
For point \( A \):
- \( x_1 = 2 \) (the x-coordinate of point \( A \))
- \( y_1 = 4 \) (the y-coordinate of point \( A \))
For point \( B \):
- \( x_2 = 8 \) (the x-coordinate of point \( B \))
- \( y_2 = 6 \) (the y-coordinate of point \( B \))
### Step 2: Use the Midpoint Formula
The formula to find the midpoint \( M \) of a line segment defined by points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) is:
\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
### Step 3: Plug in the Coordinates
Now we will substitute the coordinates of points \( A \) and \( B \) into the formula:
\[
M = \left( \frac{2 + 8}{2}, \frac{4 + 6}{2} \right)
\]
### Step 4: Calculate the x-coordinate
First, calculate the x-coordinate of \( M \):
\[
\frac{2 + 8}{2} = \frac{10}{2} = 5
\]
### Step 5: Calculate the y-coordinate
Next, calculate the y-coordinate of \( M \):
\[
\frac{4 + 6}{2} = \frac{10}{2} = 5
\]
### Final Result
Putting it all together, we find the midpoint \( M \):
\[
M = (5, 5)
\]
So, the midpoint of segment \( AB \) is **(5, 5)**.
To find the **midpoint** of a line segment connecting two points \( A \) and \( B \), we use a specific formula. The points given are:
- Point \( A \) has coordinates \( (2, 4) \).
- Point \( B \) has coordinates \( (8, 6) \).
### Step 1: Identify the Coordinates
For point \( A \):
- \( x_1 = 2 \) (the x-coordinate of point \( A \))
- \( y_1 = 4 \) (the y-coordinate of point \( A \))
For point \( B \):
- \( x_2 = 8 \) (the x-coordinate of point \( B \))
- \( y_2 = 6 \) (the y-coordinate of point \( B \))
### Step 2: Use the Midpoint Formula
The formula to find the midpoint \( M \) of a line segment defined by points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) is:
\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
### Step 3: Plug in the Coordinates
Now we will substitute the coordinates of points \( A \) and \( B \) into the formula:
\[
M = \left( \frac{2 + 8}{2}, \frac{4 + 6}{2} \right)
\]
### Step 4: Calculate the x-coordinate
First, calculate the x-coordinate of \( M \):
\[
\frac{2 + 8}{2} = \frac{10}{2} = 5
\]
### Step 5: Calculate the y-coordinate
Next, calculate the y-coordinate of \( M \):
\[
\frac{4 + 6}{2} = \frac{10}{2} = 5
\]
### Final Result
Putting it all together, we find the midpoint \( M \):
\[
M = (5, 5)
\]
So, the midpoint of segment \( AB \) is **(5, 5)**.
Answer
Type how you explain it better. For example, \[
\frac{4 + 6}{2} = \frac{10}{2} = 5
\]. That doesn't make sense.
\frac{4 + 6}{2} = \frac{10}{2} = 5
\]. That doesn't make sense.
Answered by
GPT-4o mini
I apologize for the confusion! Let's clarify that step more clearly. Here's a refined explanation for finding the midpoint:
### Finding the Midpoint of a Line Segment
**Given Points:**
- Point \( A \) with coordinates \( (2, 4) \)
- Point \( B \) with coordinates \( (8, 6) \)
**Step 1: Understanding the Midpoint Formula**
The midpoint \( M \) of the line segment connecting two points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) is calculated using this formula:
\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
Here:
- \( x_1 \) and \( y_1 \) are the coordinates of point \( A \).
- \( x_2 \) and \( y_2 \) are the coordinates of point \( B \).
**Step 2: Substituting the Values**
- For point \( A \):
- \( x_1 = 2 \)
- \( y_1 = 4 \)
- For point \( B \):
- \( x_2 = 8 \)
- \( y_2 = 6 \)
Now substitute these values into the formula:
\[
M = \left( \frac{2 + 8}{2}, \frac{4 + 6}{2} \right)
\]
**Step 3: Calculating the Coordinates**
Now, let's calculate the midpoint step by step:
1. Calculate the x-coordinate of \( M \):
\[
x\text{-coordinate} = \frac{2 + 8}{2}
\]
- First, add the x-coordinates: \( 2 + 8 = 10 \).
- Then divide by 2: \( \frac{10}{2} = 5 \).
2. Calculate the y-coordinate of \( M \):
\[
y\text{-coordinate} = \frac{4 + 6}{2}
\]
- First, add the y-coordinates: \( 4 + 6 = 10 \).
- Then divide by 2: \( \frac{10}{2} = 5 \).
**Step 4: Final Result**
Combining both results, the coordinates of the midpoint \( M \) are:
\[
M = (5, 5)
\]
Thus, the midpoint of segment \( AB \) is **(5, 5)**.
### Finding the Midpoint of a Line Segment
**Given Points:**
- Point \( A \) with coordinates \( (2, 4) \)
- Point \( B \) with coordinates \( (8, 6) \)
**Step 1: Understanding the Midpoint Formula**
The midpoint \( M \) of the line segment connecting two points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) is calculated using this formula:
\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
Here:
- \( x_1 \) and \( y_1 \) are the coordinates of point \( A \).
- \( x_2 \) and \( y_2 \) are the coordinates of point \( B \).
**Step 2: Substituting the Values**
- For point \( A \):
- \( x_1 = 2 \)
- \( y_1 = 4 \)
- For point \( B \):
- \( x_2 = 8 \)
- \( y_2 = 6 \)
Now substitute these values into the formula:
\[
M = \left( \frac{2 + 8}{2}, \frac{4 + 6}{2} \right)
\]
**Step 3: Calculating the Coordinates**
Now, let's calculate the midpoint step by step:
1. Calculate the x-coordinate of \( M \):
\[
x\text{-coordinate} = \frac{2 + 8}{2}
\]
- First, add the x-coordinates: \( 2 + 8 = 10 \).
- Then divide by 2: \( \frac{10}{2} = 5 \).
2. Calculate the y-coordinate of \( M \):
\[
y\text{-coordinate} = \frac{4 + 6}{2}
\]
- First, add the y-coordinates: \( 4 + 6 = 10 \).
- Then divide by 2: \( \frac{10}{2} = 5 \).
**Step 4: Final Result**
Combining both results, the coordinates of the midpoint \( M \) are:
\[
M = (5, 5)
\]
Thus, the midpoint of segment \( AB \) is **(5, 5)**.
Answer
You did not fix it
Answered by
GPT-4o mini
I apologize for the oversight. Let's present the calculations step-by-step in a clearer manner and clarify any potential confusion. Here’s a structured approach to finding the midpoint with clear explanations for each calculation:
### Finding the Midpoint of a Line Segment
**Given Points:**
- Point \( A \) has coordinates \( (2, 4) \).
- Point \( B \) has coordinates \( (8, 6) \).
### Step 1: Midpoint Formula
To find the midpoint \( M \) of the segment that connects points \( A \) and \( B \), we use the following formula:
\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
### Step 2: Identify Coordinates
For point \( A \):
- \( x_1 = 2 \) (the x-coordinate of point \( A \))
- \( y_1 = 4 \) (the y-coordinate of point \( A \))
For point \( B \):
- \( x_2 = 8 \) (the x-coordinate of point \( B \))
- \( y_2 = 6 \) (the y-coordinate of point \( B \))
### Step 3: Substitute into the Formula
Now we substitute the coordinates of points \( A \) and \( B \) into the midpoint formula:
\[
M = \left( \frac{2 + 8}{2}, \frac{4 + 6}{2} \right)
\]
### Step 4: Calculate the Midpoint
1. **Calculate the x-coordinate:**
- Add the x-coordinates:
\[
2 + 8 = 10
\]
- Divide by 2:
\[
\frac{10}{2} = 5
\]
2. **Calculate the y-coordinate:**
- Add the y-coordinates:
\[
4 + 6 = 10
\]
- Divide by 2:
\[
\frac{10}{2} = 5
\]
### Step 5: Combine the Results
Now we can write the final midpoint:
\[
M = (5, 5)
\]
**Conclusion:**
The midpoint of the segment \( AB \) is \( (5, 5) \).
Thank you for your patience, and I hope this explanation is much clearer!
### Finding the Midpoint of a Line Segment
**Given Points:**
- Point \( A \) has coordinates \( (2, 4) \).
- Point \( B \) has coordinates \( (8, 6) \).
### Step 1: Midpoint Formula
To find the midpoint \( M \) of the segment that connects points \( A \) and \( B \), we use the following formula:
\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
### Step 2: Identify Coordinates
For point \( A \):
- \( x_1 = 2 \) (the x-coordinate of point \( A \))
- \( y_1 = 4 \) (the y-coordinate of point \( A \))
For point \( B \):
- \( x_2 = 8 \) (the x-coordinate of point \( B \))
- \( y_2 = 6 \) (the y-coordinate of point \( B \))
### Step 3: Substitute into the Formula
Now we substitute the coordinates of points \( A \) and \( B \) into the midpoint formula:
\[
M = \left( \frac{2 + 8}{2}, \frac{4 + 6}{2} \right)
\]
### Step 4: Calculate the Midpoint
1. **Calculate the x-coordinate:**
- Add the x-coordinates:
\[
2 + 8 = 10
\]
- Divide by 2:
\[
\frac{10}{2} = 5
\]
2. **Calculate the y-coordinate:**
- Add the y-coordinates:
\[
4 + 6 = 10
\]
- Divide by 2:
\[
\frac{10}{2} = 5
\]
### Step 5: Combine the Results
Now we can write the final midpoint:
\[
M = (5, 5)
\]
**Conclusion:**
The midpoint of the segment \( AB \) is \( (5, 5) \).
Thank you for your patience, and I hope this explanation is much clearer!
Answer
The midpoint \( M \) of a segment with endpoints \( A(x_1, y_1) \) and \( B(x_2, y_2) \) can be found using the formula:
\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
For the given points \( A(2, 4) \) and \( B(8, 6) \):
- \( x_1 = 2 \)
- \( y_1 = 4 \)
- \( x_2 = 8 \)
- \( y_2 = 6 \)
Now, we can plug these values into the formula:
\[
M = \left( \frac{2 + 8}{2}, \frac{4 + 6}{2} \right)
\]
\[
M = \left( \frac{10}{2}, \frac{10}{2} \right)
\]
\[
M = (5, 5)
\]
The midpoint of segment AB is \( (5, 5) \). Please type this better so I can understand what you're saying. Use the right symbols.
\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
For the given points \( A(2, 4) \) and \( B(8, 6) \):
- \( x_1 = 2 \)
- \( y_1 = 4 \)
- \( x_2 = 8 \)
- \( y_2 = 6 \)
Now, we can plug these values into the formula:
\[
M = \left( \frac{2 + 8}{2}, \frac{4 + 6}{2} \right)
\]
\[
M = \left( \frac{10}{2}, \frac{10}{2} \right)
\]
\[
M = (5, 5)
\]
The midpoint of segment AB is \( (5, 5) \). Please type this better so I can understand what you're saying. Use the right symbols.
Answered by
GPT-4o mini
Certainly! Here’s a clearer and more structured explanation using appropriate symbols and formatting:
### Finding the Midpoint of a Line Segment
**Definition of Midpoint:**
The midpoint \( M \) of a line segment connecting two points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) is calculated using the formula:
\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
**Given Points:**
- Point \( A \) has coordinates \( (2, 4) \)
- Therefore, \( x_1 = 2 \) and \( y_1 = 4 \)
- Point \( B \) has coordinates \( (8, 6) \)
- Therefore, \( x_2 = 8 \) and \( y_2 = 6 \)
### Step 1: Substitute the Values into the Formula
Let's substitute the values of the coordinates into the midpoint formula:
\[
M = \left( \frac{2 + 8}{2}, \frac{4 + 6}{2} \right)
\]
### Step 2: Calculate the Midpoint
**Calculating the x-coordinate of \( M \):**
1. Add \( x_1 \) and \( x_2 \):
\[
2 + 8 = 10
\]
2. Divide the result by 2:
\[
\frac{10}{2} = 5
\]
**Calculating the y-coordinate of \( M \):**
1. Add \( y_1 \) and \( y_2 \):
\[
4 + 6 = 10
\]
2. Divide the result by 2:
\[
\frac{10}{2} = 5
\]
### Step 3: Combine the Results
Combining both coordinates, we find the midpoint:
\[
M = (5, 5)
\]
### Conclusion
Thus, the midpoint of segment \( AB \) is
\[
\boxed{(5, 5)}
\]
This structure shows each step clearly, making it easy to follow the calculations leading to the result. If you have any further questions or need additional clarifications, feel free to ask!
### Finding the Midpoint of a Line Segment
**Definition of Midpoint:**
The midpoint \( M \) of a line segment connecting two points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) is calculated using the formula:
\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
**Given Points:**
- Point \( A \) has coordinates \( (2, 4) \)
- Therefore, \( x_1 = 2 \) and \( y_1 = 4 \)
- Point \( B \) has coordinates \( (8, 6) \)
- Therefore, \( x_2 = 8 \) and \( y_2 = 6 \)
### Step 1: Substitute the Values into the Formula
Let's substitute the values of the coordinates into the midpoint formula:
\[
M = \left( \frac{2 + 8}{2}, \frac{4 + 6}{2} \right)
\]
### Step 2: Calculate the Midpoint
**Calculating the x-coordinate of \( M \):**
1. Add \( x_1 \) and \( x_2 \):
\[
2 + 8 = 10
\]
2. Divide the result by 2:
\[
\frac{10}{2} = 5
\]
**Calculating the y-coordinate of \( M \):**
1. Add \( y_1 \) and \( y_2 \):
\[
4 + 6 = 10
\]
2. Divide the result by 2:
\[
\frac{10}{2} = 5
\]
### Step 3: Combine the Results
Combining both coordinates, we find the midpoint:
\[
M = (5, 5)
\]
### Conclusion
Thus, the midpoint of segment \( AB \) is
\[
\boxed{(5, 5)}
\]
This structure shows each step clearly, making it easy to follow the calculations leading to the result. If you have any further questions or need additional clarifications, feel free to ask!
Answer
Stop using "/" and "]"
Answered by
GPT-4o mini
I apologize for any confusion! Let's rewrite everything without using slashes or brackets and ensure it's clear:
### Finding the Midpoint of a Line Segment
**Definition of Midpoint:**
The midpoint, denoted as M, of a line segment connecting two points A and B is calculated using the formula:
M equals the point where the x-coordinates of A and B are added together, divided by 2; and the y-coordinates of A and B are added together, divided by 2.
**Given Points:**
- Point A has coordinates (2, 4)
- Here, the x-coordinate of A is 2 and the y-coordinate of A is 4.
- Point B has coordinates (8, 6)
- Here, the x-coordinate of B is 8 and the y-coordinate of B is 6.
### Step 1: Substitute the Values into the Formula
To find the midpoint M, we substitute the coordinates of A and B into the midpoint formula:
M equals the point where the sum of the x-coordinates of A and B, which is 2 plus 8, is divided by 2, and the sum of the y-coordinates of A and B, which is 4 plus 6, is also divided by 2.
### Step 2: Perform the Calculations
**Calculating the x-coordinate of M:**
1. First, add the x-coordinates:
2 plus 8 equals 10.
2. Next, divide the result by 2:
10 divided by 2 equals 5.
**Calculating the y-coordinate of M:**
1. First, add the y-coordinates:
4 plus 6 equals 10.
2. Next, divide the result by 2:
10 divided by 2 equals 5.
### Step 3: Combine the Results
Combining both results gives us the midpoint:
M equals (5, 5).
### Conclusion
Thus, the midpoint of segment AB is (5, 5).
I hope this format is clearer for you! Let me know if there's anything else you would like me to clarify.
### Finding the Midpoint of a Line Segment
**Definition of Midpoint:**
The midpoint, denoted as M, of a line segment connecting two points A and B is calculated using the formula:
M equals the point where the x-coordinates of A and B are added together, divided by 2; and the y-coordinates of A and B are added together, divided by 2.
**Given Points:**
- Point A has coordinates (2, 4)
- Here, the x-coordinate of A is 2 and the y-coordinate of A is 4.
- Point B has coordinates (8, 6)
- Here, the x-coordinate of B is 8 and the y-coordinate of B is 6.
### Step 1: Substitute the Values into the Formula
To find the midpoint M, we substitute the coordinates of A and B into the midpoint formula:
M equals the point where the sum of the x-coordinates of A and B, which is 2 plus 8, is divided by 2, and the sum of the y-coordinates of A and B, which is 4 plus 6, is also divided by 2.
### Step 2: Perform the Calculations
**Calculating the x-coordinate of M:**
1. First, add the x-coordinates:
2 plus 8 equals 10.
2. Next, divide the result by 2:
10 divided by 2 equals 5.
**Calculating the y-coordinate of M:**
1. First, add the y-coordinates:
4 plus 6 equals 10.
2. Next, divide the result by 2:
10 divided by 2 equals 5.
### Step 3: Combine the Results
Combining both results gives us the midpoint:
M equals (5, 5).
### Conclusion
Thus, the midpoint of segment AB is (5, 5).
I hope this format is clearer for you! Let me know if there's anything else you would like me to clarify.