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: \(d=(6−2)^2+(1−5)^2−−−−−−−−−−−−−−−√\) matches the correct setup.

Thus, the correct choice is:

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