DaQuan marks two points on the coordinate plane. One point is L(4,2) and the other point is M (7,6). What is the correct way for DaQuan to set up the distance formula?

Answer 1

The distance formula between two points \( L(x_1, y_1) \) and \( M(x_2, y_2) \) in the coordinate plane is given by:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

In this case, the coordinates of the points are:

• \( L(4, 2) \) where \( x_1 = 4 \) and \( y_1 = 2 \)
• \( M(7, 6) \) where \( x_2 = 7 \) and \( y_2 = 6 \)

Substituting these values into the distance formula, we set it up as follows:

\[ d = \sqrt{(7 - 4)^2 + (6 - 2)^2} \]

This simplifies to:

\[ d = \sqrt{(3)^2 + (4)^2} \]

So, DaQuan sets up the distance formula as:

\[ d = \sqrt{(7 - 4)^2 + (6 - 2)^2} \]