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
O 100
O 9.22
O 10
To find the distance between two points using the Pythagorean theorem, we need to calculate the length of each side of the right triangle formed by the two points.
The horizontal distance between the points is 5 - (-1) = 6 units.
The vertical distance between the points is -2 - 6 = -8 units.
To find the length between the two points, we can use the Pythagorean theorem formula: c^2 = a^2 + b^2, where c is the length between the points, and a and b are the horizontal and vertical distances.
c^2 = 6^2 + (-8)^2
c^2 = 36 + 64
c^2 = 100
Taking the square root of both sides, we get:
c = √100
c = 10
Therefore, the length between the two points is 10 units.
The correct answer is:
O 10
To apply the Pythagorean Theorem, we need to find the distance between the two given points on a Cartesian plane.
The Pythagorean Theorem states that in a right-angled 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.
In this case, the two given points are (-1, 6) and (5, -2). We can consider these points as the two endpoints of a line segment, forming the two sides of a right-angled triangle, with the third side being the hypotenuse.
To find the length between the points, we need to find the lengths of the two sides of the right-angled triangle formed.
Using the distance formula for two points in a plane, we can find the length of the sides as follows:
Length of horizontal side (base):
= |x2 - x1|
= |5 - (-1)|
= |5 + 1|
= 6
Length of vertical side (height):
= |y2 - y1|
= |-2 - 6|
= |-2 + (-6)|
= 8
Now, we can use the Pythagorean Theorem to find the length of the hypotenuse (distance between the two points):
Hypotenuse^2 = base^2 + height^2
Hypotenuse^2 = 6^2 + 8^2
Hypotenuse^2 = 36 + 64
Hypotenuse^2 = 100
Taking the square root of both sides to find the length of the hypotenuse:
Hypotenuse = sqrt(100)
Hypotenuse ≈ 10
Therefore, the length between the points (-1, 6) and (5, -2) is approximately 10.
To apply the Pythagorean Theorem to find the length between two points, we need to calculate the distance along the x-axis and the distance along the y-axis. The theorem states that the square of the hypotenuse (the longest side) of a right triangle is equal to the sum of the squares of the other two sides.
The distance along the x-axis is the difference between the x-coordinates of the two points: 5 - (-1) = 6.
The distance along the y-axis is the difference between the y-coordinates of the two points: -2 - 6 = -8.
Now, we can use these values to calculate the length between the two points using the Pythagorean Theorem.
According to the theorem, the length between the two points is √(x² + y²), where x and y are the distances along the x-axis and y-axis, respectively.
So, substituting the values, we get √(6² + (-8)²) = √(36 + 64) = √(100) = 10.
Therefore, the length between the points (-1, 6) and (5, -2) is 10 units. Since the question asks us to round the answer to the nearest hundredth, the final answer is 10.00.