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)
Responses

d=(6−7)2+(2−4)2−−−−−−−−−−−−−−−√
d is equal to square root of open paren 6 minus 7 close paren squared plus open paren 2 minus 4 close paren squared end root

d=(2−4)2+(6−7)2−−−−−−−−−−−−−−−√
d is equal to square root of open paren 2 minus 4 close paren squared plus open paren 6 minus 7 close paren squared end root

d=(2−7)2+(4−6)2−−−−−−−−−−−−−−−√
d is equal to square root of open paren 2 minus 7 close paren squared plus open paren 4 minus 6 close paren squared end root

d=(4−7)2+(2−6)2−−−−−−−−−−−−−−−√

Answer 1

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

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

In our 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 \( y_2 = 6 \)

Plugging in the values into the formula, we get:

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

This simplifies to:

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

Looking at the response options, the correct formulation for the distance calculation is the one that reflects this calculation correctly.

None of the provided options match this exact setup. However, if we rewrite the expressions, we can see the following provides the correct distance setup:

**Correct Formulation**:

\[
d=\sqrt{(4−7)^2+(2−6)^2}
\]

Thus, the final choice indicating this setup would be:

- \( d=(4−7)^{2}+(2−6)^{2} \)

So the correct option is:

**d=(4−7)²+(2−6)²−−−−−−−−−−−−−−−√**