Question

On a coordinate plane, point E is at the point negative 8 comma negative 7 and point F is at the point 9 comma 5.

Question
What is the distance between the points E and F?

Answer options with 4 options
A.
29

B.
StartRoot 5 EndRoot

C.
StartRoot 29 Endroot

D.
StartRoot 433 EndRoot

Answer 1

To find the distance between the points \( E(-8, -7) \) and \( F(9, 5) \), you can use the distance formula:

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

In this case:
- \( x_1 = -8 \)
- \( y_1 = -7 \)
- \( x_2 = 9 \)
- \( y_2 = 5 \)

Now plug in the values:

\[
d = \sqrt{(9 - (-8))^2 + (5 - (-7))^2}
\]

Calculate the differences:

\[
d = \sqrt{(9 + 8)^2 + (5 + 7)^2}
\]
\[
d = \sqrt{(17)^2 + (12)^2}
\]

Now calculate the squares:

\[
d = \sqrt{289 + 144}
\]
\[
d = \sqrt{433}
\]

Thus, the distance between points E and F is:

\[
\sqrt{433}
\]

The correct answer is:

**D. \( \sqrt{433} \)**