Question

How should the distance formula be set up to determine the distance between the points  (−5,−10)  and  (4,8) ?(1 point)Responsesd=(−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 rootd=(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 rootd=(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 rootd=(−5−4)2+(−10−8)2−−−−−−−−−−−−−−−−−−−√

Answer 1

To find the distance \(d\) between the points \((-5, -10)\) and \((4, 8)\), we use the distance formula given by:

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

Where \((x_1, y_1) = (-5, -10)\) and \((x_2, y_2) = (4, 8)\).

Now let's set up the formula with the values of the points:

1. \(x_1 = -5\), \(y_1 = -10\)
2. \(x_2 = 4\), \(y_2 = 8\)

Plugging these values into the distance formula:

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

This simplifies to:

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

So:

\[
d = \sqrt{(9)^2 + (18)^2}
\]

Therefore, the correct option that sets up the distance formula for these points is:

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

So, the final answer should be:

\[
d=(−5−4)^2+(−10−8)^2−−−−−−−−−−−−−−−−−−−√
\]