Question
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)
100
10
9.22
14
100
10
9.22
14
Answers
GPT 3.5
To find the distance between two points, we can use 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). We can treat these points as the vertices of a right triangle, with the distance between them as the hypotenuse.
The difference in the x-coordinates is 5 - (-1) = 6.
The difference in the y-coordinates is -2 - 6 = -8.
We can set up a right triangle and calculate the distance between the two points using the Pythagorean Theorem:
d^2 = 6^2 + (-8)^2
d^2 = 36 + 64
d^2 = 100
Taking the square root of both sides:
d = √100
d = 10
Therefore, the distance between the two points (-1, 6) and (5, -2) is 10. This value is already rounded, so the answer is:
10.
In this case, the two points are (-1, 6) and (5, -2). We can treat these points as the vertices of a right triangle, with the distance between them as the hypotenuse.
The difference in the x-coordinates is 5 - (-1) = 6.
The difference in the y-coordinates is -2 - 6 = -8.
We can set up a right triangle and calculate the distance between the two points using the Pythagorean Theorem:
d^2 = 6^2 + (-8)^2
d^2 = 36 + 64
d^2 = 100
Taking the square root of both sides:
d = √100
d = 10
Therefore, the distance between the two points (-1, 6) and (5, -2) is 10. This value is already rounded, so the answer is:
10.