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

Question

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

Answer 1

To use the distance formula correctly, you need to have the coordinates of the two points involved. The distance formula is given as:

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

For the points \(L(4, 2)\) and \(M(7, 6)\), we can assign the coordinates as follows:

• Point \(L\) has coordinates \((x_1, y_1) = (4, 2)\)
• Point \(M\) has coordinates \((x_2, y_2) = (7, 6)\)

Substituting these coordinates into the distance formula, we would set it up as:

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

or written out, it can be expressed as:

\[ d = \sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2} = \sqrt{(6 - 2)^2 + (7 - 4)^2} \]

This aligns with option:

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

So the correct way for DaQuan to set up the distance formula is to use:

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

None of the provided options match this exactly, but this is the correct setup based on the coordinates given. If you're looking for the expected option based on the differences calculated, note that it matches up to the format provided, with the coordinates aligning correctly for \((y_2 - y_1)\) and \((x_2 - x_1)\).