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=(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−−−−−−−−−−−−−−−√
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=(2−4)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 for the distance \(d\) given by:

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

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

Plugging in these coordinates into the distance formula:

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

Calculating the differences:

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

So, the correct setup from the options provided 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

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