Question

Distance in the Coordinate Plane Quick Check 1 of 51 of 5 Items 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) Responses d=(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 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−−−−−−−−−−−−−−−−−−√ 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 Skip to navigation page 17 of 17 Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.

Answer 1

To find the distance between points $E$ and $F$ using the distance formula, you need to identify the coordinates of these two points. The distance formula is given by:

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

Where $(x_1,y_1)$ and $(x_2,y_2)$ are the coordinates of points $E$ and $F$. Assuming the coordinates for $E$ are $(2,5)$ and for $F$ are $(6,1)$, we can set up the formula as follows:

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

So, looking at your options:

• Option 5: $d=(6-2{)}^2+(1-5{)}^2---------------\surd$ matches the correct setup.

Thus, the correct choice is:

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