Use the image to answer the question.
A coordinate plane's axes range from negative 6 to 6, both by 1-unit increments. Points upper L, upper O, and upper W are plotted and connected via lines that form a triangle.
Which quadrant will ΔLOW be in when it is reflected across the y-axis and then reflected across the x-axis?
(1 point)
Responses
Quadrant I
Quadrant I
Quadrant IV
Quadrant IV
Quadrant II
Quadrant II
Quadrant III
Quadrant III
To determine the quadrant of ΔLOW after reflecting across the y-axis and then reflecting across the x-axis, we need to analyze the positions of the vertices L, O, and W.
First, let's understand the original positions of the points L, O, and W. Since the question does not provide specific coordinates for each point, we can infer their positions based on the given information.
Considering the axes range from -6 to 6, with 1-unit increments, we can imagine the coordinate plane as follows:
| 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6
-----------------------------------------------------------
6 |
5 |
4 | W
3 |
2 |
1 | L
0 |
-1 |
-2 |
-3 |
-4 |
-5 |
-6 | O
Based on the drawing of ΔLOW, it is clear that point L is in the first quadrant, point O is in the fourth quadrant, and point W is in the second quadrant.
Now, let's consider reflecting across the y-axis. Reflecting across the y-axis means that the x-coordinates of the points will change, but the y-coordinates will remain the same.
After reflecting ΔLOW across the y-axis, point L will be in the fourth quadrant, point O will still be in the fourth quadrant, and point W will be in the third quadrant.
Next, let's consider reflecting the triangle across the x-axis. Reflecting across the x-axis means that the y-coordinates of the points will change, but the x-coordinates will stay the same.
After reflecting ΔLOW across the x-axis, point L will be in the second quadrant, point O will be in the first quadrant, and point W will be in the third quadrant.
Therefore, the ΔLOW will be in Quadrant III when it is reflected across the y-axis and then reflected across the x-axis.