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? (1 point)

d=(6-7)2+(2-4)2 d=(2-4)2+(6-7)2 d=(2-7)2+(4-6)2 d=√(4-7)2+(2-6)2

Answer 1

To correctly set up the distance formula between points \( L(4, 2) \) and \( M(7, 6) \), we can use the distance formula, which is given by:

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

In this case:
- \( (x_1, y_1) = (4, 2) \)
- \( (x_2, y_2) = (7, 6) \)

Substituting these values into the formula:

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

This simplifies to:

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

Now, let's compare this to the options given:

1. **\( d = (6 - 7)^2 + (2 - 4)^2 \)**
2. **\( d = (2 - 4)^2 + (6 - 7)^2 \)**
3. **\( d = (2 - 7)^2 + (4 - 6)^2 \)**
4. **\( d = \sqrt{(4 - 7)^2 + (2 - 6)^2} \)**

The correct set up should reflect the distance formula using the coordinates of points L and M.

Considering the options, **the fourth option: \( d = \sqrt{(4 - 7)^2 + (2 - 6)^2} \)** is the most accurate for calculating the distance between points L and M, but with minor corrections in the signs for the coordinates as they reflect the input correctly.

Thus, the correct form for finding the distance is:

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

Therefore, the fourth option can also be viewed as a valid expression.