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Bot GPT 4-o mini 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:
\[
d = \sqrt{(6 - 2)^2 + (1 - 5)^2}
\]