Question

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

To set up the distance formula between two points \( L(x_1, y_1) \) and \( M(x_2, y_2) \), you can use the formula:

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

In this case, point \( L \) has coordinates \( (4, 2) \) and point \( M \) has coordinates \( (7, 6) \). Therefore:

- \( x_1 = 4 \)
- \( y_1 = 2 \)
- \( x_2 = 7 \)
- \( y_2 = 6 \)

Now, substituting these values into the distance formula gives us:

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

This can be simplified as follows:

\[
d = \sqrt{(3)^2 + (4)^2}
\]
\[
d = \sqrt{9 + 16}
\]
\[
d = \sqrt{25}
\]
\[
d = 5
\]

So, the correct way for DaQuan to set up the distance formula is:

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

And the distance \( d \) between points \( L \) and \( M \) is \( 5 \).