Question

How should the distance formula be set up to determine the distance between the points (−5,−10) and (4,8) ?(1 point) Responses d=(5−4)2−(10−8)2−−−−−−−−−−−−−−−−√ d is equal to square root of open paren 5 minus 4 close paren squared minus open paren 10 minus 8 close paren squared end root d=(−5−4)2−(−10−8)2−−−−−−−−−−−−−−−−−−−√ d is equal to square root of open paren negative 5 minus 4 close paren squared minus open paren negative 10 minus 8 close paren squared end root d=(5−4)2+(10−8)2−−−−−−−−−−−−−−−−√ d is equal to square root of open paren 5 minus 4 close paren squared plus open paren 10 minus 8 close paren squared end root d=(−5−4)2+(−10−8)2−−−−−−−−−−−−−−−−−−−√

Answer 1

To determine the distance between the points \((-5, -10)\) and \( (4, 8) \), you would use the distance formula, which is given by:

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

In this case, let \((x_1, y_1) = (-5, -10)\) and \((x_2, y_2) = (4, 8)\). Plugging in these coordinates into the distance formula:

\[
d = \sqrt{(4 - (-5))^2 + (8 - (-10))^2}
\]

This can be simplified to:

\[
d = \sqrt{(4 + 5)^2 + (8 + 10)^2} = \sqrt{(9)^2 + (18)^2} = \sqrt{81 + 324} = \sqrt{405}
\]

Therefore, the correctly set up distance formula is:

\[
d = \sqrt{(4 - (-5))^2 + (8 - (-10))^2}
\]

Among the provided responses, the one that matches this setup is:

\[
d = \sqrt{(-5 - 4)^2 + (-10 - 8)^2}
\]

This option is equivalent because it correctly reflects the points being used in the distance formula (with the signs correctly considered).

So, the final correct answer is:

\[
d = \sqrt{(-5 - 4)^2 + (-10 - 8)^2}
\]