Find the distance between these two points using the Pythagorean Theorem.

Question

Which choice is correct?

(1 point)
Responses

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

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

62−−√+32=25−−√square root of 6 squared end root plus 3 squared is equal to square root of 25
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Answer 1

To find the distance between two points using the Pythagorean Theorem, you can use the formula:

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

where \( (x_1, y_1) \) and \( (x_2, y_2) \) are the coordinates of the two points.

Let’s analyze the given options:

1. First Response: \( 52 + 72 = \sqrt{136} \)

   • Looks incorrect. This uses incorrect addition instead of calculating squares.

2. Second Response: \( \sqrt{(6^2 + 10^2)} = \sqrt{136} \)

   • This implies points at (0,0) and (6,10). This is valid since \( 6^2 + 10^2 = 36 + 100 = 136 \) and thus, \( \sqrt{136} \) is correct.

3. Third Response: \( \sqrt{3^2} - 5 = \sqrt{20} \)

   • Does not follow the Pythagorean theorem correctly.

4. Fourth Response: \( \sqrt{6^2} + 3 = \sqrt{25} \)

   • Incorrect application of the theorem.

The correct choice is the second response:

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