Demonstrating the properties of rotations, if a line segment with endpoints (0, -3) and (0, -7) is rotated 90 degrees clockwise, what is an endpoint of this rotated segment?
Wrong, that is not an answer.
Still wrong, the given answers are:
(0, 3)
(0, 7)
(3, 0)
(-3, 0)
Demonstrating the properties of rotations, if a line segment with endpoints (0, -3) and (0, -7) is rotated 90 degrees clockwise, what is an endpoint of this rotated segment?
(0, 3)
(0, 7)
(3, 0)
(-3, 0)
To rotate a point 90 degrees clockwise about the origin, you need to swap the x and y-coordinates and change the sign of the new x-coordinate.
Let's perform this transformation on the endpoint (0, -7):
New x-coordinate: -(-7) = 7
New y-coordinate: 0
Therefore, the endpoint of the rotated segment is (7, 0).
Apologies for the incorrect answer. Let's correctly determine the endpoint of the rotated segment.
To rotate a point 90 degrees clockwise about the origin, we can use the following rotation formula:
x' = x * cos(θ) - y * sin(θ)
y' = x * sin(θ) + y * cos(θ)
Since we want to rotate the segment 90 degrees clockwise, we need to use θ = -90 degrees or -π/2 radians.
The original endpoint is (0, -7). Substituting these values into the rotation formulas, we get:
x' = 0 * cos(-π/2) - (-7) * sin(-π/2) = 0 * 0 - (-7) * (-1) = -7
y' = 0 * sin(-π/2) + (-7) * cos(-π/2) = 0 * (-1) + (-7) * 0 = 0
Therefore, the endpoint of the rotated segment is (-7, 0).
Apologies for the confusion. Let's correctly determine the endpoint of the rotated segment.
To rotate a point 90 degrees clockwise about the origin, we can use the following rotation formulas:
x' = x * cos(θ) + y * sin(θ)
y' = -x * sin(θ) + y * cos(θ)
Since we want to rotate the segment 90 degrees clockwise, we need to use θ = -90 degrees or -π/2 radians.
Let's use the first given endpoint (0, -7) and substitute these values into the rotation formulas:
x' = 0 * cos(-π/2) + (-7) * sin(-π/2) = 0 * 0 + (-7) * (-1) = 0 + 7 = 7
y' = -(0 * sin(-π/2)) + (-7) * cos(-π/2) = -0 + (-7) * 0 = 0 - 0 = 0
Therefore, the endpoint of the rotated segment is (7, 0).
So, we conclude that the endpoint of the given line segment after rotating 90 degrees clockwise is (7, 0).
Apologies for the incorrect responses. Let's correctly determine the endpoint of the rotated segment.
To rotate a point 90 degrees clockwise about the origin, we need to swap the x and y coordinates and change the sign of the new y coordinate.
First, let's take the endpoint (0, -7) and perform the rotation:
New x-coordinate: -(-7) = 7
New y-coordinate: 0
Therefore, the endpoint of the rotated segment is (7, 0).
Hence, the correct answer is (7, 0).