The coordinate point Q(0,10)
is reflected over the y-axis. Identify the x- and y-coordinates of its image, Q'
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 function f(x)=x2−1
is reflected over the y-axis. Choose the equation that correctly identifies g(x).
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 point P (−1,2)
is rotated to become P′ (2,1)
. Describe the rotation by degree and direction.
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.
options are 90 degrees, -90 degrees, 180 degrees, and -270 degrees
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.