find the image (0,0) after two reflections first across y=3 and then across X-axis
ammar
Did you try asking the image? They might reflect back on what happened!
To find the image of a point (0,0) after two reflections, let's break down the problem step by step:
Step 1:
The first reflection is across the equation y = 3.
Since the point (0,0) is on the x-axis, the line y = 3 does not intersect it. When reflecting a point across a vertical line, such as y = 3, it remains at the same x-coordinate but changes its y-coordinate.
For the point (0,0), the reflection across y = 3 would result in a point with the same x-coordinate of 0, but with a y-coordinate that is the same distance below y = 3 as it is above y = 3. Therefore, the new point after the first reflection is (0, -6).
Step 2:
The second reflection is across the x-axis.
Reflecting a point across the x-axis changes only the sign of the y-coordinate, while the x-coordinate remains the same.
For the point (0, -6), reflecting it across the x-axis would result in a new point with the same x-coordinate of 0, but with a y-coordinate that is the opposite sign. Therefore, the final image after the second reflection is (0, 6).
So, the image of the point (0,0) after two reflections, first across y = 3 and then across the x-axis, is (0, 6).
To find the image of a point after two reflections, first across a line and then across the X-axis, you need to follow these steps:
1. Begin with the original point (0,0).
2. Reflect the point across the line y=3.
- The line y=3 is a horizontal line parallel to the X-axis, passing through y=3.
- To reflect a point across a horizontal line, keep the y-coordinate the same and change the sign of the x-coordinate.
- Since the original point (0,0) lies on the line y=3, the reflection across this line will result in the same point (0,0).
3. Reflect the result of step 2 across the X-axis.
- The X-axis is a horizontal line passing through y=0.
- To reflect a point across the X-axis, keep the x-coordinate the same and change the sign of the y-coordinate.
- Applying this to the result of step 2, which is (0,0), the reflection across the X-axis will also result in (0,0).
Therefore, after two reflections, first across the line y=3 and then across the X-axis, the image of the point (0,0) remains unchanged, and the image point is also (0,0).
easily done with a sketch
across y = 3
(0,0) ---> (0,6)
across the x-axis
(0,6) ---> (0, -6)
(remember that the equation of the x-axis is y = 0