We want to find the image of the given point after two reflections. Let's consider each of them one at a time.
Reflection Across the Line l_1
First we will reflect the point O(0,0) across the line y=3. To do this, let's begin by plotting the point and drawing the line of reflection on a coordinate plane.
Now we will draw a line that is perpendicular to the line of reflection and passes through O(0,0). If you need further explanation on how to draw a line that passes through a given point and is perpendicular to a given line, please refer to this explanation.
Finally, we can measure the distance from the preimage point to the line of reflection and locate the reflected image the same distance from the given line on the opposite side.
As we can see, (0,6) are the coordinates of the point after a reflection across the line y=3.
Reflection Across the Line l_2
We will now reflect the point (0,6) across the x -axis using the same reasoning as we did to perform the first reflection. Let's identify the x -axis as the new line of reflection.
Once again, we will draw a line that is perpendicular to the x -axis and passes through the point (0,6). We will also measure the distance from the point to the line to locate the reflected image the same distance from the x -axis on the opposite side.
The image of the point O(0,0) after two reflections is (0,-6).
