Question

how would you set up the distance formula to find the distance between points E and

E(1,-6) and F(2, -5)

Answer 1

not a option

Answer 2

available options:

d = \sqrt{(2 - 6)^2 + (5 - (-1)^2}

d = \sqrt{(-6 - 2)^2 + (1 - (-5))^2}

d = \sqrt{(-2)+ 6)^2 + (5 + 1) ^2}

d = \sqrt{(6 - 2)^2 + (1 - 5)^2}

Answer 3

To find the distance between two points \( E(x_1, y_1) \) and \( F(x_2, y_2) \) in a coordinate plane, you can use the distance formula, which is:

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

For the points \( E(1, -6) \) and \( F(2, -5) \), we assign the coordinates as follows:

- \( x_1 = 1 \)
- \( y_1 = -6 \)
- \( x_2 = 2 \)
- \( y_2 = -5 \)

Now, plug these values into the distance formula:

\[
d = \sqrt{(2 - 1)^2 + (-5 - (-6))^2}
\]

Calculating each part:

1. \( (2 - 1)^2 = 1^2 = 1 \)
2. \( -5 - (-6) = -5 + 6 = 1 \) and \( (1)^2 = 1^2 = 1 \)

Now substitute these values back into the formula:

\[
d = \sqrt{1 + 1} = \sqrt{2}
\]

Thus, the distance between points \( E(1, -6) \) and \( F(2, -5) \) is \( \sqrt{2} \).

Answer 4

I apologize for any misunderstanding. Let's verify the calculations for the distance between the points \( E(1, -6) \) and \( F(2, -5) \).

1. Using the distance formula:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

2. Substitute the coordinates of points \( E \) and \( F \):
- \( x_1 = 1 \)
- \( y_1 = -6 \)
- \( x_2 = 2 \)
- \( y_2 = -5 \)

3. Plugging the values into the distance formula:
\[
d = \sqrt{(2 - 1)^2 + (-5 - (-6))^2}
\]
This simplifies to:
\[
d = \sqrt{(1)^2 + (-5 + 6)^2}
\]
Which becomes:
\[
d = \sqrt{(1)^2 + (1)^2} = \sqrt{1 + 1} = \sqrt{2}
\]

The calculated distance between points \( E(1, -6) \) and \( F(2, -5) \) is indeed \( \sqrt{2} \).

If \( \sqrt{2} \) is not an option, please provide the available options, and I can help you verify if the calculations align with any other consideration or context.

Answer 5

To find the distance between points \( E(1, -6) \) and \( F(2, -5) \), let's rewrite the distance formula correctly and identify which option could be equivalent.

The distance formula is:

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

Where:
- \((x_1, y_1) = (1, -6)\)
- \((x_2, y_2) = (2, -5)\)

Substituting these values into the correct form of the formula:

\[
d = \sqrt{(2 - 1)^2 + (-5 - (-6))^2}
\]

Calculating step-by-step we previously found:

\[
d = \sqrt{(1)^2 + (1)^2} = \sqrt{1 + 1} = \sqrt{2}
\]

Now, let's analyze the provided options:

1. **Option 1:** \( d = \sqrt{(2 - 6)^2 + (5 - (-1))^2} \)
This is not correct based on the coordinates.

2. **Option 2:** \( d = \sqrt{(-6 - 2)^2 + (1 - (-5))^2} \)
This uses incorrect coordinates; it should be \( (-6 - 1) \) instead of \( (-6 - 2) \).

3. **Option 3:** \( d = \sqrt{(-2 + 6)^2 + (5 + 1)^2} \)
This is not matched to the points \(E\) and \(F\).

4. **Option 4:** \( d = \sqrt{(6 - 2)^2 + (1 - 5)^2} \)
This does not match the coordinates either.

None of the options seem to represent the distance correctly based on the coordinates of points \(E(1, -6)\) and \(F(2, -5)\).

However, since you seem to be looking for a correct structure to represent the distance calculation, you could point out that the correct form should be:

\[
d = \sqrt{(2 - 1)^2 + (-5 - (-6))^2}
\]

If you need help correcting any of the options or if more options are available, please let me know!