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

Answer 1

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

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

In this case, \( L(4, 2) \) has coordinates \( (x_1, y_1) = (4, 2) \) and \( M(7, 6) \) has coordinates \( (x_2, y_2) = (7, 6) \).

Now substituting the 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, rewriting it in the format presented in the options, we focus on each choice. The correct setup would be:

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

This matches the first option:

**d = √((4−7)² + (2−6)²)** (which corresponds to your option 1).

So the correct choice is:

**d=(4−7)²+(2−6)²−−−−−−−−−−−−−−−√**.