The distance formula between two points \( L(x_1, y_1) \) and \( M(x_2, y_2) \) in the coordinate plane is given by:
\[
d = \sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}
\]
In your case, the points are \( L(4, 2) \) and \( M(7, 6) \). Therefore, you need to use the coordinates as follows:
- \( x_1 = 4 \), \( y_1 = 2 \)
- \( x_2 = 7 \), \( y_2 = 6 \)
Substituting these values into the distance formula gives:
\[
d = \sqrt{(6 - 2)^2 + (7 - 4)^2}
\]
This simplifies to:
\[
d = \sqrt{(4)^2 + (3)^2} = \sqrt{16 + 9} = \sqrt{25} = 5
\]
Checking against the provided responses, the correct setup corresponding to the distance between points \( L(4, 2) \) and \( M(7, 6) \) is:
\[
d = \sqrt{(6 - 2)^2 + (7 - 4)^2}
\]
So the appropriate answer choice from your options is:
**d = \sqrt{(6 - 2)^2 + (7 - 4)^2}**
However, it seems that option is not available directly. But the similar version might be present as the setup using either (x1, y1) and (x2, y2) correctly. Please make sure whether modifications happen on variables in the options you provided but the correct structure follows \( d = \sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2} \) adjustments to pointwise displacement correctly.