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

5.74
5 point 7 4

8.06
8 point 0 6

65
65

11

Answer 1

The length between (2,7) and (-2,0) can be found using the Pythagorean Theorem, which states that for any right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Let's label the points as (x1, y1) = (2,7) and (x2, y2) = (-2,0).

The length (d) between these two points can be calculated using the formula:

d = √( (x2-x1)^2 + (y2-y1)^2 )

Substituting the values:
d = √( (-2-2)^2 + (0-7)^2 )
d = √( (-4)^2 + (-7)^2 )
d = √( 16 + 49 )
d = √65

Rounded to the nearest hundredth, the length between (2,7) and (-2,0) is approximately 8.06.