Question

Apply the Pythagorean Theorem to find the length between (2,7)
and (−2, 0)
. Round your answer to the nearest hundredth, if necessary.
Responses

11
11

8.06
8 point 0 6

5.74
5 point 7 4

65

Answer 1

The Pythagorean Theorem is used to find the length of the hypotenuse of a right triangle, which in this context is the distance between two points on a Cartesian coordinate system. The formula to find the distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

Given the points \((2,7)\) and \((-2, 0)\), we will use the formula to find the distance between them:

\[ d = \sqrt{(-2 - 2)^2 + (0 - 7)^2} \]
\[ d = \sqrt{(-4)^2 + (-7)^2} \]
\[ d = \sqrt{16 + 49} \]
\[ d = \sqrt{65} \]

The distance is the square root of 65. To round to the nearest hundredth:

\[ d \approx \sqrt{65} \approx 8.06 \]

So the length between the points \((2,7)\) and \((-2, 0)\) rounded to the nearest hundredth is approximately 8.06.