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)
Responses
10
10
9.22
9.22
14
14
100
The length between (-1, 6) and (5, -2) can be found by applying the Pythagorean Theorem. The formula for the Pythagorean Theorem is:
c^2 = a^2 + b^2
where c is the length of the hypotenuse and a and b are the lengths of the other two sides of the right triangle.
In this case, we can consider the difference in x-coordinates (-1 - 5 = -6) as one side of the triangle, and the difference in y-coordinates (6 - (-2) = 8) as the other side of the triangle.
Using the Pythagorean Theorem, we can calculate the length of the hypotenuse:
c^2 = (-6)^2 + 8^2
c^2 = 36 + 64
c^2 = 100
Taking the square root of both sides, we get:
c = 10
Therefore, the length between (-1, 6) and (5, -2) is 10.
To find the length between two points (-1, 6) and (5, -2), we can use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
First, we need to find the length of the vertical side, which is the difference in the y-coordinates: -2 - 6 = -8.
Next, we need to find the length of the horizontal side, which is the difference in the x-coordinates: 5 - (-1) = 6.
Using these values, we can form a right triangle with the vertical side as the height, the horizontal side as the base, and the length we want to find as the hypotenuse.
Using the Pythagorean Theorem, the length of the hypotenuse can be found as follows:
hypotenuse^2 = height^2 + base^2
hypotenuse^2 = (-8)^2 + 6^2
hypotenuse^2 = 64 + 36
hypotenuse^2 = 100
Taking the square root of both sides to solve for the hypotenuse (length), we get:
hypotenuse = √100
hypotenuse = 10
Therefore, the length between (-1, 6) and (5, -2) is 10.
To apply the Pythagorean Theorem to find the distance between two points, we need to use the formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
In this case, the coordinates are (-1, 6) and (5, -2).
We substitute the values into the formula:
d = sqrt((5 - (-1))^2 + (-2 - 6)^2)
= sqrt((6)^2 + (-8)^2)
= sqrt(36 + 64)
= sqrt(100)
= 10
Therefore, the distance between the points (-1, 6) and (5, -2) is 10 units.