Question

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

Which choice is correct?

(1 point)
Responses

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

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−−√+32=25−−√

Answer 1

To find the distance between the points (-3, 5) and (7, -1), we can use the distance formula, which is derived from the Pythagorean Theorem. The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by:

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

In this case, the coordinates are:
- \( (x_1, y_1) = (-3, 5) \)
- \( (x_2, y_2) = (7, -1) \)

Now, calculate the differences:

\[
x_2 - x_1 = 7 - (-3) = 7 + 3 = 10
\]

\[
y_2 - y_1 = -1 - 5 = -6
\]

Then, plug these values into the distance formula:

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

Calculating the squares:

\[
(10)^2 = 100
\]
\[
(-6)^2 = 36
\]

Now add them together:

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

So, the distance between the two points is \( \sqrt{136} \).

Now let's examine the response options to find the correct choice:

1. **(62+102)−−−−−−−−−√=136−−−√**
- This option states \( \sqrt{6^2 + 10^2} = \sqrt{136} \), which is not correct since we found the differences to be 10 and -6, not 6 and 10.

2. **32−−√−52=20−−√**
- This option doesn't make sense in the context of distance calculation. It does not correlate to our computation.

3. **52+72=136−−−√**
- This option states \( 5^2 + 7^2 = \sqrt{136} \) which is also incorrect because we have \( 10 \) as first and \(-6\) as second value.

4. **62−−√+32=25−−√**
- This option does not make sense in the context of distance.

None of the response options correctly represent the distance calculation we performed using the points (-3, 5) and (7, -1).

The correct answer should have been \( \sqrt{(10)^2 + (-6)^2} = \sqrt{136} \). If the options contain an error, it's advisable to check again or provide a correct set of options.