Asked by TheDarkArtist
The coordinate point Q(0,10)
is reflected over the y-axis. Identify the x- and y-coordinates of its image, Q'
is reflected over the y-axis. Identify the x- and y-coordinates of its image, Q'
Answers
Answered by
GPT 3.5
When a point is reflected over the y-axis, the x-coordinate is negated while the y-coordinate remains the same.
The x-coordinate of Q is 0. When reflected over the y-axis, the x-coordinate becomes -0. Therefore, the x-coordinate of Q' is -0.
The y-coordinate of Q is 10. When reflected over the y-axis, the y-coordinate remains the same. Therefore, the y-coordinate of Q' is 10.
So, the x-coordinate of Q' is -0, and the y-coordinate of Q' is 10.
The x-coordinate of Q is 0. When reflected over the y-axis, the x-coordinate becomes -0. Therefore, the x-coordinate of Q' is -0.
The y-coordinate of Q is 10. When reflected over the y-axis, the y-coordinate remains the same. Therefore, the y-coordinate of Q' is 10.
So, the x-coordinate of Q' is -0, and the y-coordinate of Q' is 10.
Answered by
TheDarkArtist
The function f(x)=x2−1
is reflected over the y-axis. Choose the equation that correctly identifies g(x).
is reflected over the y-axis. Choose the equation that correctly identifies g(x).
Answered by
GPT 3.5
To reflect a function over the y-axis, the sign of the x-term changes.
The original function is f(x) = x^2 - 1.
When this is reflected over the y-axis, the x term becomes -x.
So, the equation for the reflected function g(x) is g(x) = (-x)^2 - 1.
Simplifying that, we get g(x) = x^2 - 1.
Therefore, the equation that correctly identifies g(x) is g(x) = x^2 - 1.
The original function is f(x) = x^2 - 1.
When this is reflected over the y-axis, the x term becomes -x.
So, the equation for the reflected function g(x) is g(x) = (-x)^2 - 1.
Simplifying that, we get g(x) = x^2 - 1.
Therefore, the equation that correctly identifies g(x) is g(x) = x^2 - 1.
Answered by
TheDarkArtist
The point P (−1,2)
is rotated to become P′ (2,1)
. Describe the rotation by degree and direction.
is rotated to become P′ (2,1)
. Describe the rotation by degree and direction.
Answered by
GPT 3.5
To describe the rotation of a point, we need to determine the angle and direction of rotation.
Given that the point P (-1, 2) is rotated to become P' (2, 1), we can determine the angle and direction of rotation using the following steps:
1. Determine the change in x and y coordinates.
Δx = x' - x = 2 - (-1) = 3
Δy = y' - y = 1 - 2 = -1
2. Calculate the tangent of the angle of rotation.
tan(θ) = Δy / Δx = -1 / 3
3. Find the angle of rotation.
θ = atan(-1/3) = -18.43 degrees (approximately)
Since the y-coordinate decreases and the x-coordinate increases, we can determine that the rotation is in a clockwise direction.
Therefore, the rotation of point P (-1, 2) to P' (2, 1) is a clockwise rotation of approximately 18.43 degrees.
Given that the point P (-1, 2) is rotated to become P' (2, 1), we can determine the angle and direction of rotation using the following steps:
1. Determine the change in x and y coordinates.
Δx = x' - x = 2 - (-1) = 3
Δy = y' - y = 1 - 2 = -1
2. Calculate the tangent of the angle of rotation.
tan(θ) = Δy / Δx = -1 / 3
3. Find the angle of rotation.
θ = atan(-1/3) = -18.43 degrees (approximately)
Since the y-coordinate decreases and the x-coordinate increases, we can determine that the rotation is in a clockwise direction.
Therefore, the rotation of point P (-1, 2) to P' (2, 1) is a clockwise rotation of approximately 18.43 degrees.
Answered by
TheDarkArtist
options are 90 degrees, -90 degrees, 180 degrees, and -270 degrees
Answered by
GPT 3.5
If the options are limited to 90 degrees, -90 degrees, 180 degrees, and -270 degrees, we need to reassess the angle of rotation.
Given that P (-1, 2) is rotated to P' (2, 1), we can determine the change in x and y coordinates as follows:
Δx = x' - x = 2 - (-1) = 3
Δy = y' - y = 1 - 2 = -1
If we compare the change in x to the change in y, we can determine the angle of rotation.
If Δx = Δy, the angle of rotation is 45 degrees or -135 degrees.
If Δx = -Δy, the angle of rotation is -45 degrees or 135 degrees.
Since none of the given options match these angles, it is not possible to describe the rotation by degree and direction using the provided options.
Given that P (-1, 2) is rotated to P' (2, 1), we can determine the change in x and y coordinates as follows:
Δx = x' - x = 2 - (-1) = 3
Δy = y' - y = 1 - 2 = -1
If we compare the change in x to the change in y, we can determine the angle of rotation.
If Δx = Δy, the angle of rotation is 45 degrees or -135 degrees.
If Δx = -Δy, the angle of rotation is -45 degrees or 135 degrees.
Since none of the given options match these angles, it is not possible to describe the rotation by degree and direction using the provided options.