Question

A straight, solid line connects plotted points E and F on a coordinate plane. The line slopes downward from left to right. Point E is left parenthesis negative 6 comma 1 right parenthesis. Point F is left parenthesis 2 comma negative 5 right parenthesis.
How would you set up the distance formula to find the distance between points E
and F
.

(1 point)
Responses

d=((−2)+6)2+(5+1)2−−−−−−−−−−−−−−−−−−√
d is equal to square root of open paren negative 2 plus 6 close paren squared plus open paren 5 plus 1 close paren squared end root

d=(6−2)2+(1−5)2−−−−−−−−−−−−−−−√
d is equal to square root of open paren 6 minus 2 close paren squared plus open paren 1 minus 5 close paren squared end root

d=(−6−2)2+(1−(−5))2−−−−−−−−−−−−−−−−−−−√
d is equal to square root of open paren negative 6 minus 2 close paren squared plus open paren 1 minus negative 5 close paren squared end root

d=(2−6)2+(5−1)2−−−−−−−−−−−−−−−√

Answer 1

To find the distance between points E \((-6, 1)\) and F \((2, -5)\) using the distance formula, we set it up as follows:

The distance formula is:

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

Where \((x_1, y_1)\) is point E \((-6, 1)\) and \((x_2, y_2)\) is point F \((2, -5)\).

Substituting the coordinates into the formula gives us:

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

This can be written as:

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

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

Thus, the correct option that sets up the distance formula to find the distance between points E and F is:

**None of the provided options are correct.**

But the closest to the correct setup, ignoring signs, would actually be:

**d= \(\sqrt{(2 + 6)^2 + (-5 - 1)^2}\)** (not provided in the choices).