Question

Find the distance and length of the segment AB. A is, (0,4) and B is, (6,-2)

Answer 1

Can you show how you got it in a better way? I can't understand what you're showing.

Answer 2

They way you are typing it in is not understandable. Like for example, \( 6\sqrt{2} \).

Answer 3

To find the distance and length of the segment AB between the points A(0, 4) and B(6, -2), we can use the distance formula, which is given by:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

In this case:
- \( A(x_1, y_1) = (0, 4) \)
- \( B(x_2, y_2) = (6, -2) \)

Now, substitute the coordinates into the distance formula:

1. Calculate the differences:
- \( x_2 - x_1 = 6 - 0 = 6 \)
- \( y_2 - y_1 = -2 - 4 = -6 \)

2. Apply the differences in the formula:
\[
d = \sqrt{(6)^2 + (-6)^2}
\]

3. Calculate the squares:
\[
d = \sqrt{36 + 36}
\]
\[
d = \sqrt{72}
\]

4. Simplify the square root:
\[
d = \sqrt{36 \times 2} = 6\sqrt{2}
\]

Therefore, the distance and length of segment AB is \(6\sqrt{2}\) units.

Answer 4

Sure! Let's break it down step by step in a clearer way. To find the distance between points A and B, we use the distance formula. Here’s how to do it:

### Step 1: Identify the Points
We have two points:
- Point A: \( A(0, 4) \)
- Point B: \( B(6, -2) \)

### Step 2: Use the Distance Formula
The distance formula is given by:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Where:
- \( (x_1, y_1) = (0, 4) \) (coordinates of point A)
- \( (x_2, y_2) = (6, -2) \) (coordinates of point B)

### Step 3: Substitute the Coordinates
Now, substitute the coordinates into the formula:

- \( x_1 = 0 \)
- \( y_1 = 4 \)
- \( x_2 = 6 \)
- \( y_2 = -2 \)

Substituting these values in gives us:

\[
d = \sqrt{(6 - 0)^2 + (-2 - 4)^2}
\]

### Step 4: Simplify Inside the Square Root
Calculate the differences:

1. For the x-coordinates:
\[
6 - 0 = 6
\]

2. For the y-coordinates:
\[
-2 - 4 = -6
\]

Now, plug these into the formula:

\[
d = \sqrt{(6)^2 + (-6)^2}
\]

### Step 5: Calculate the Squares
Now we calculate the squares:

1. \( (6)^2 = 36 \)
2. \( (-6)^2 = 36 \)

So we have:

\[
d = \sqrt{36 + 36}
\]

### Step 6: Add the Values
Add the squared values:

\[
d = \sqrt{72}
\]

### Step 7: Simplify the Square Root
Finally, we can simplify the square root:

\[
\sqrt{72} = \sqrt{36 \times 2} = 6\sqrt{2}
\]

### Final Answer
The distance between points A and B is \( 6\sqrt{2} \) units.

I hope this step-by-step explanation helps you understand how to calculate the distance!

Answer 5

I apologize for any confusion! Let's present the calculations more straightforwardly without special characters. Here’s the process of calculating the distance between points A(0, 4) and B(6, -2) in a clearer way.

### Step 1: Identify the points

- Point A: (0, 4)
- Point B: (6, -2)

### Step 2: Use the distance formula

The formula to find the distance (d) between two points (x1, y1) and (x2, y2) is:

d = √[(x2 - x1)² + (y2 - y1)²]

### Step 3: Identify the coordinates

For our points:

- x1 = 0, y1 = 4
- x2 = 6, y2 = -2

### Step 4: Substitute the coordinates into the formula

d = √[(6 - 0)² + (-2 - 4)²]

### Step 5: Simplify the calculation

1. First, calculate the differences:
- x2 - x1 = 6 - 0 = 6
- y2 - y1 = -2 - 4 = -6

So, we substitute these results back into the formula:

d = √[(6)² + (-6)²]

2. Next, calculate the squares:
- (6)² = 36
- (-6)² = 36

Now, plug in the squared values:

d = √[36 + 36]

### Step 6: Simplify further

d = √[72]

### Step 7: Breaking down √72

√72 can be simplified. You can break it down like this:
√72 = √(36 × 2)

3. Since √36 = 6, we have:

d = 6√2

### Final Answer

So, the distance between points A(0, 4) and B(6, -2) is **6 times the square root of 2** or approximately **8.49** when using a calculator.

If you have any more questions or need further clarification, feel free to ask!