Question

Distance in the Coordinate Plane Quick Check 2 of 52 of 5 Items 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=(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 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 Skip to navigation page 17 of 17 Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.

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, we can assign:

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

Plugging these coordinates into the formula gives:

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

This simplifies to:

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

Looking at the options provided, the correct way for DaQuan to set up the distance formula is:

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

However, this option may not be explicitly listed. Among the given options, this formulation could manifest in several equivalent forms depending on the order of subtraction, provided they yield the same squared results after simplification:

1. The closest representation of the formulation is:

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

So the correct response from the options provided is:

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