To apply the Pythagorean Theorem to find the length between two points, we need to find the horizontal and vertical distances between the two points.
The horizontal distance is found by subtracting the x-coordinates of the two points.
Horizontal distance = 7 - 2 = 5
The vertical distance is found by subtracting the y-coordinates of the two points.
Vertical distance = 3 - 5 = -2
Now, we can apply the Pythagorean Theorem, which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides.
Using the horizontal and vertical distances as the two sides of a right triangle, we have:
Hypotenuse^2 = Horizontal distance^2 + Vertical distance^2
Hypotenuse^2 = 5^2 + (-2)^2
Hypotenuse^2 = 25 + 4
Hypotenuse^2 = 29
To find the length of the hypotenuse, we take the square root of both sides:
Hypotenuse = sqrt(29)
Rounding to the nearest hundredth, Hypotenuse ≈ 5.39
Therefore, the length between (2, 5) and (7, 3) is approximately 5.39 units.
Apply the Pythagorean Theorem to find the length between ( 2 , 5 ) and ( 7 , 3 ) . Round your answer to the nearest hundredth, if necessary.(1 point)
3 answers
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)
To apply the Pythagorean Theorem to find the length between two points, we need to find the horizontal and vertical distances between the two points.
The horizontal distance is found by subtracting the x-coordinates of the two points.
Horizontal distance = 5 - (-1) = 6
The vertical distance is found by subtracting the y-coordinates of the two points.
Vertical distance = (-2) - 6 = -8
Now, we can apply the Pythagorean Theorem, which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides.
Using the horizontal and vertical distances as the two sides of a right triangle, we have:
Hypotenuse^2 = Horizontal distance^2 + Vertical distance^2
Hypotenuse^2 = 6^2 + (-8)^2
Hypotenuse^2 = 36 + 64
Hypotenuse^2 = 100
To find the length of the hypotenuse, we take the square root of both sides:
Hypotenuse = sqrt(100)
Rounding to the nearest hundredth, Hypotenuse ≈ 10.00
Therefore, the length between (-1, 6) and (5, -2) is approximately 10.00 units.
The horizontal distance is found by subtracting the x-coordinates of the two points.
Horizontal distance = 5 - (-1) = 6
The vertical distance is found by subtracting the y-coordinates of the two points.
Vertical distance = (-2) - 6 = -8
Now, we can apply the Pythagorean Theorem, which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides.
Using the horizontal and vertical distances as the two sides of a right triangle, we have:
Hypotenuse^2 = Horizontal distance^2 + Vertical distance^2
Hypotenuse^2 = 6^2 + (-8)^2
Hypotenuse^2 = 36 + 64
Hypotenuse^2 = 100
To find the length of the hypotenuse, we take the square root of both sides:
Hypotenuse = sqrt(100)
Rounding to the nearest hundredth, Hypotenuse ≈ 10.00
Therefore, the length between (-1, 6) and (5, -2) is approximately 10.00 units.
2 answers