Question

Apply the Pythagorean Theorem to find the length between (2,7)
and (−2, 0)
. Round your answer to the nearest hundredth, if necessary.(1 point)
Responses

11
11

65
65

5.74
5 point 7 4

8.06

Answer 1

Let's apply the Pythagorean Theorem to find the distance between the points (2,7) and (−2,0). The distance formula, which derives from the Pythagorean Theorem for the coordinates on a Cartesian plane, is:

Distance = √[(x2 - x1)² + (y2 - y1)²]

Where (x1, y1) are the coordinates of the first point and (x2, y2) are the coordinates of the second point.

For our points, (2,7) and (−2,0), we have:

x1 = 2, y1 = 7
x2 = −2, y2 = 0

Now plug these values into the distance formula:

Distance = √[(−2 - 2)² + (0 - 7)²]
Distance = √[(-4)² + (-7)²]
Distance = √[16 + 49]
Distance = √[65]
Distance ≈ 8.06

So, the distance between the two points, rounded to the nearest hundredth, is approximately 8.06.