To set up the distance formula between the points L (4, 2) and M (7, 6), we use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
where \((x_1, y_1)\) are the coordinates of point L and \((x_2, y_2)\) are the coordinates of point M.
In this case:
- \(x_1 = 4\), \(y_1 = 2\) (coordinates of L)
- \(x_2 = 7\), \(y_2 = 6\) (coordinates of M)
Substituting these values into the distance formula gives:
\[ d = \sqrt{(7 - 4)^2 + (6 - 2)^2} \] \[ d = \sqrt{(3)^2 + (4)^2} \] \[ d = \sqrt{9 + 16} \] \[ d = \sqrt{25} \] \[ d = 5 \]
None of the options provided matches the correct distance formula directly. However, the closest option, if we look at the structure, appears to be related to the calculations of the distances in terms of (x1, y1) and (x2, y2).
It seems like there's a typo or misrepresentation in the provided options, but to set up the distance formula correctly, it should be:
\[ d = \sqrt{(7 - 4)^2 + (6 - 2)^2} \]
To ensure clarity, the correct formulation resembles more:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Please adjust accordingly based on the specific answers provided.