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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.