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

Question

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=(2−4)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

Answer 1

To set up the distance formula between two points \( L(x_1, y_1) \) and \( M(x_2, y_2) \), the correct formula is:

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

Given the points \( L(4, 2) \) and \( M(7, 6) \):

• \( x_1 = 4 \), \( y_1 = 2 \)
• \( x_2 = 7 \), \( y_2 = 6 \)

Substituting these values into the distance formula gives:

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

This simplifies to:

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

Now, looking at the responses provided, the correct setup should be:

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

So the correct response from your options is:

d = square root of (4 minus 7) squared plus (2 minus 6) squared.