Apply the Pythagorean Theorem to find the length between (-1, 6) and
(5, 2). Round your answer to the nearest hundredth, if necessary. (1 point)
-
O 14
○ 10
100
9.22
The distance between two points in a plane can be found using the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the two points are (-1, 6) and (5, 2), which can be visualized as forming a right triangle with the line connecting the two points as the hypotenuse.
The horizontal distance between the two points is the difference in x-coordinates: 5 - (-1) = 6
The vertical distance between the two points is the difference in y-coordinates: 2 - 6 = -4
Now, we can use the Pythagorean Theorem to find the length of the hypotenuse, which is the distance between the two points:
c^2 = 6^2 + (-4)^2
c^2 = 36 + 16
c^2 = 52
c ≈ √52
c ≈ 7.21
Therefore, the distance between the points (-1, 6) and (5, 2) is approximately 7.21 units.