Apply the Pythagorean Theorem to find the length of the diagonal of the square. Round your answer to the nearest hundredth, if necessary.
(1 point)
Responses
4
4
4.24
4.24
8
8
2.83
2.83
To find the length of the diagonal of a square, we can apply the Pythagorean Theorem, which 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.
In the case of a square, the two sides are equal in length, and each forms a right angle with the diagonal.
Let's represent the length of one side of the square as "s" and the length of the diagonal as "d."
Using the Pythagorean Theorem, we have:
s^2 + s^2 = d^2
2s^2 = d^2
Taking the square root on both sides:
sqrt(2s^2) = sqrt(d^2)
sqrt(2) * s = d
Therefore, the length of the diagonal of the square is equal to the square root of 2 times the length of one side.
Rounding to the nearest hundredth if necessary, the length of the diagonal is approximately 2.83.
To apply the Pythagorean Theorem to find the distance between two points, we need to consider the coordinates of those points as the lengths of the sides of a right triangle in a Cartesian coordinate system.
Let's represent the first point as (x1, y1) = (2, 5) and the second point as (x2, y2) = (7, 3).
The length between these two points can be found using the formula:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the values:
distance = sqrt((7 - 2)^2 + (3 - 5)^2)
distance = sqrt(5^2 + (-2)^2)
distance = sqrt(25 + 4)
distance = sqrt(29)
Rounded to the nearest hundredth, the distance between the points (2, 5) and (7, 3) is approximately 5.38.
To apply the Pythagorean Theorem to find the distance between two points, we need to consider the coordinates of those points as the lengths of the sides of a right triangle in a Cartesian coordinate system.
Let's represent the first point as (x1, y1) = (-1, 6) and the second point as (x2, y2) = (5, -2).
The length between these two points can be found using the formula:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the values:
distance = sqrt((5 - (-1))^2 + (-2 - 6)^2)
distance = sqrt((5 + 1)^2 + (-2 - 6)^2)
distance = sqrt(6^2 + (-8)^2)
distance = sqrt(36 + 64)
distance = sqrt(100)
Rounded to the nearest hundredth, the distance between the points (-1, 6) and (5, -2) is approximately 10.
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)
Responses
2.65
2.65
5.38
5.38
4.58
4.58
29
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
14
14
100
100
9.22
Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth, if necessary.
(1 point)
Responses
9
9
6:40
6:40
41
41
5.57