Question

Question content area top
Part 1
Find the distance between the pair of points.
Upper E left parenthesis 10 comma negative 2 right parenthesisE(10,−2)​, Upper F left parenthesis negative 2 comma 3 right parenthesisF(−2,3)
Question content area bottom
Part 1
ddequals=enter your response here

Answer 1

To find the distance between two points \( E(10, -2) \) and \( F(-2, 3) \) in a 2-dimensional plane, we use the distance formula given by:

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

Here, \( (x_1, y_1) \) is the coordinates of point E and \( (x_2, y_2) \) is the coordinates of point F:

- \( E(10, -2) \): \( x_1 = 10 \) and \( y_1 = -2 \)
- \( F(-2, 3) \): \( x_2 = -2 \) and \( y_2 = 3 \)

Now, we can plug the values into the distance formula:

\[
d = \sqrt{((-2) - 10)^2 + (3 - (-2))^2}
\]

Calculating the differences:

\[
d = \sqrt{(-12)^2 + (5)^2}
\]

Calculating the squares:

\[
d = \sqrt{144 + 25}
\]

Now, add the results:

\[
d = \sqrt{169}
\]

Taking the square root:

\[
d = 13
\]

Thus, the distance between the points \( E \) and \( F \) is:

\[
\boxed{13}
\]