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

Answer 1

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

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

Here, the coordinates of points L and M are:
- \( L(x_1, y_1) = (4, 2) \)
- \( M(x_2, y_2) = (7, 6) \)

Substituting the coordinates into the distance formula:

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

So we have:

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

The correct setup of the distance formula from the given options is:

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

Thus, the correct response is:

**d = (4−7)² + (2−6)²** (which corresponds to the last option).