Question

(-3,5) (7,-1)
Find the distance between these two points using the Pythagorean Theorem.

Which choice is correct?

(1 point)
Responses

62−−√+32=25−−√
square root of 6 squared end root plus 3 squared is equal to square root of 25

32−−√−52=20−−√
square root of 3 squared end root minus 5 squared is equal to square root of 20

52+72=136−−−√
5 squared plus 7 squared is equal to square root of 136

(62+102)−−−−−−−−−√=136−−−√
square root of open paren 6 squared plus 10 squared close paren end root is equal to square root of 136
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Answer 1

To find the distance between the points (-3, 5) and (7, -1) using the Pythagorean Theorem, we'll use the distance formula:

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

Here, \((x_1, y_1) = (-3, 5)\) and \((x_2, y_2) = (7, -1)\).

First, calculate \(x_2 - x_1\) and \(y_2 - y_1\):

\[
x_2 - x_1 = 7 - (-3) = 7 + 3 = 10
\]
\[
y_2 - y_1 = -1 - 5 = -6
\]

Now, plug these values into the distance formula:

\[
d = \sqrt{(10)^2 + (-6)^2}
\]

Now calculate the squares:

\[
d = \sqrt{100 + 36}
\]
\[
d = \sqrt{136}
\]

Now, let's check which of the provided choices matches our calculation.

1. \(\sqrt{6^2 + 3^2} = \sqrt{36 + 9} = \sqrt{45}\) (Incorrect)
2. \(\sqrt{3^2 - 5^2} = \sqrt{9 - 25} = \sqrt{-16}\) (Incorrect)
3. \(5^2 + 7^2 = 25 + 49 = 74\) (Incorrect)
4. \(\sqrt{(6^2 + 10^2)} = \sqrt{36 + 100} = \sqrt{136}\) (Correct)

So the correct choice is:

\[
(\sqrt{(6^2 + 10^2)} = \sqrt{136})
\]