Use the image to answer the question.How would you set up the distance formula to find the distance between points E and F .(1 point)Responsesd=(−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 rootd=((−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 rootd=(2−6)2+(5−1)2−−−−−−−−−−−−−−−√d is equal to square root of open paren 2 minus 6 close paren squared plus open paren 5 minus 1 close paren squared end rootd=(6−2)2+(1−5)2−−−−−−−−−−−−−−−√

Question

Use the image to answer the question.How would you set up the distance formula to find the distance between points  E  and  F .(1 point)Responsesd=(−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 rootd=((−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 rootd=(2−6)2+(5−1)2−−−−−−−−−−−−−−−√d is equal to square root of open paren 2 minus 6 close paren squared plus open paren 5 minus 1 close paren squared end rootd=(6−2)2+(1−5)2−−−−−−−−−−−−−−−√

GPT-4o mini · Answer

To set up the distance formula between points \( E \) and \( F \), we need to know the coordinates of those points. The distance formula is given by:

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

Assuming point \( E \) has coordinates \( (x_1, y_1) \) and point \( F \) has coordinates \( (x_2, y_2) \), you would replace \( x_1, y_1, x_2, \) and \( y_2 \) with the actual coordinate values of points \( E \) and \( F \).

Looking at the provided responses, without the specifics of the coordinates, we can derive which response is correctly using the distance formula based on their structures.

However, since the actual coordinates for points \( E \) and \( F \) are unclear from the question context, you would want to select the response that follows the order of coordinates corresponding to points \( E \) and \( F \).

Typically, the distance calculation should follow the standard method shown in the equation above, meaning you need to identify the correct coordinates from the responses given.

Let's analyze the responses you provided:

Option 1: \( d = \sqrt{(-6 - 2)^2 + (1 - (-5))^2} \)
Option 2: \( d = \sqrt{(-2 + 6)^2 + (5 + 1)^2} \)
Option 3: \( d = \sqrt{(2 - 6)^2 + (5 - 1)^2} \)
Option 4: \( d = \sqrt{(6 - 2)^2 + (1 - 5)^2} \)

Choose the response that matches your coordinates correctly. The correct setup depends on substituting the correct coordinates from points \( E \) and \( F \) into the distance formula structured above.