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

Question

. 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=(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=(2−7)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 for the points L(4, 2) and M(7, 6), we will use the distance formula, which is given by:

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

Here, \( (x_1, y_1) \) are the coordinates of point L and \( (x_2, y_2) \) are the coordinates of point M.

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

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

Using the distance formula:

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

This simplifies to:

\[ d = \sqrt{(3)^2 + (4)^2} \]

None of the provided responses are the exact distance formula in this case, with the correct substitution of coordinates. However, the correct setup should start with \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).

To look at the options given:

1. \( d = \sqrt{(2 - 4)^2 + (6 - 7)^2} \) → This one is incorrect.
2. \( d = \sqrt{(4 - 7)^2 + (2 - 6)^2} \) → This one is actually correct since it gives the distance in the same effective way.
3. \( d = \sqrt{(2 - 7)^2 + (4 - 6)^2} \) → This one is incorrect.
4. \( d = \sqrt{(6 - 7)^2 + (2 - 4)^2} \) → This one is incorrect.

The correct choice is:

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

This reflects the proper calculation of distance between the points.