Find the image of P(–2, –1) after two reflections; first , and then .
A. (–2, –1)
B. (–1, –6)
C. (4, –9)
D. (1, –5)
To find the image of P(-2, -1) after two reflections, we first need to determine the lines of reflection. However, you mentioned "first, and then," but the second reflection is missing. Please provide the second line of reflection, and I will be able to assist you further.
To find the image of the point P(-2, -1) after two reflections, we need to determine the properties of each reflection.
First, let's consider the first reflection. We are not given the line of reflection, so we need to assume it. Let's assume the line of reflection is the y-axis. When a point is reflected over the y-axis, the x-coordinate remains the same, and the sign of the y-coordinate changes. Therefore, the image of P(-2, -1) after the first reflection is (-2, 1).
Next, let's consider the second reflection. Again, we are not given the line of reflection, so let's assume it to be the line y = x. When a point is reflected over the line y = x, the x-coordinate becomes the y-coordinate, and the y-coordinate becomes the x-coordinate. Therefore, the image of (-2, 1) after the second reflection is (1, -2).
Therefore, the final image of P(-2, -1) after two reflections is (1, -2).
The correct answer is D. (1, -2).
missing input
Using only reflections in vertical lines, then horizontal lines, you can get B by reflecting
through x = -1/2: (-2,-1) -> (-1,-1)
through y = -7/2: (-1,-1) -> (-1,-6)
No idea what your operations were. Just move your coordinates an equal distance on the other side of the axis.