The distance formula for two points \( L(x_1, y_1) \) and \( M(x_2, y_2) \) in the coordinate plane is given by:
\[ d = \sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2} \]
For the points \( L(4, 2) \) and \( M(7, 6) \), we identify:
- \( (x_1, y_1) = (4, 2) \)
- \( (x_2, y_2) = (7, 6) \)
Plugging the coordinates into the distance formula, we have:
\[ d = \sqrt{(6 - 2)^2 + (7 - 4)^2} \]
This translates to:
\[ d = \sqrt{(2)^2 + (3)^2} \]
Now let's analyze the options provided:
- d = √(6 − 7)² + (2 − 4)² - This is incorrect, as the coordinates are mixed up.
- d = √(2 − 4)² + (6 − 7)² - This is incorrect as well, for similar reasons.
- d = √(2 − 7)² + (4 − 6)² - This is incorrect, as this swaps the points.
- d = √(4 − 7)² + (2 − 6)² - This is the correct formula where \( x_1 = 4 \), \( x_2 = 7 \) and \( y_1 = 2 \), \( y_2 = 6 \).
Thus, the correct option for how DaQuan should set up the distance formula is:
d = √(4 − 7)² + (2 − 6)²