Question

DaQuan marks two points on the coordinate plane. One point is L(4,2)
𝐿
(
4
,
2
)
and the other point is M(7,6)
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
=
(
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
=
(
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
=
(
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=(6−7)2+(2−4)2−−−−−−−−−−−−−−−√

Answer 1

To set up the distance formula correctly between the two points \( L(4,2) \) and \( M(7,6) \), we will use the distance formula defined as:

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

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

Substituting the coordinates into the formula, we have:

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

This is equivalent to:

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

Thus, the correct setup for the distance formula from the options provided is:

\[
d = (4 - 7)^2 + (2 - 6)^2 \quad \text{ (the first option)}
\]

Therefore, the correct response is:

**d = (4 - 7)² + (2 - 6)²**