Question

How would you set up the distance formula to find the distance between points E and F.
point E is at (-6, 1)
point F is at (2, -5)

Answer 1

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

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

For your specific points:
- Point \( E \) is at \( (-6, 1) \), so \( x_1 = -6 \) and \( y_1 = 1 \).
- Point \( F \) is at \( (2, -5) \), so \( x_2 = 2 \) and \( y_2 = -5 \).

Substituting these values into the distance formula:

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

Now, simplify inside the parentheses:

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

This further simplifies to:

\[
d = \sqrt{(8)^2 + (-6)^2}
\]

Calculating the squares:

\[
d = \sqrt{64 + 36}
\]

Now, add the two results:

\[
d = \sqrt{100}
\]

Finally, take the square root:

\[
d = 10
\]

So, the distance between points \( E \) and \( F \) is \( 10 \).