Question

How should the distance formula be set up to determine the distance between the points (−5,−10)
(
−
5
,
−
10
)
and (4,8)
(
4
,
8
)
?(1 point)
Responses

d=(−5−4)2−(−10−8)2−−−−−−−−−−−−−−−−−−−√
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
=
(
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−−−−−−−−−−−−−−−−√
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−−−−−−−−−−−−−−−−−−−√

Answer 1

To determine the distance between the points \((-5, -10)\) and \((4, 8)\), we use the distance formula:

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

In this case:
- \(x_1 = -5\)
- \(y_1 = -10\)
- \(x_2 = 4\)
- \(y_2 = 8\)

Plugging these values into the formula:

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

This simplifies to:

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

Thus:

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

This means the correct setup of the distance formula in your options is:

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

So, the correct response would be:

**d = (−5−4)² + (−10−8)²**.