DaQuan marks two points on the coordinate plane. One point is L(4,2)

Question

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 two points \( L(4,2) \) and \( M(7,6) \), we use the formula:

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

Here, \( (x_1, y_1) = (4, 2) \) and \( (x_2, y_2) = (7, 6) \).

Substituting the values into the formula, we have:

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

This simplifies to:

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

Now, looking at the provided responses, the correct way to express this using the coordinates given is:

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

Thus, the correct response is:

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.