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=(2−7)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=(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=(6−7)2+(2−4)2−−−−−−−−−−−−−−−√

Answer 1

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

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

Where:
- \( (x_1, y_1) \) are the coordinates of the first point, \( L \), which is \( (4, 2) \).
- \( (x_2, y_2) \) are the coordinates of the second point, \( M \), which is \( (7, 6) \).

Plugging in the coordinates:

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

We calculate the differences:

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

Thus, we can rewrite the distance formula as:

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

When we evaluate this, we get:

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

However, looking at the answer choices you provided, the correct setup matching the calculations above would be:

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

Thus, the correct response is:

**d = \sqrt{(4−7)² + (2−6)²}**