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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 II
Quadrant II

Quadrant III
Quadrant III

Quadrant IV
Quadrant IV
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1 answer

To determine the quadrant in which triangle ΔLOW will be after its reflections across the y-axis and then the x-axis, you'll need to follow these steps:

  1. Reflect across the y-axis: When you reflect a point (x, y) across the y-axis, the new coordinates become (-x, y). This means that the x-coordinates of all the points will change signs, while the y-coordinates will remain the same.

  2. Reflect across the x-axis: After the first reflection, when you reflect the new coordinates (-x, y) across the x-axis, the new coordinates will become (-x, -y). Here, the x-coordinates remain the same, but the y-coordinates change signs.

After both reflections, the coordinates of each point in triangle ΔLOW will have both x and y coordinates changed in sign.

Thus, if the original points of triangle ΔLOW were in Quadrant I, II, III, or IV before the reflections, they will end up in the opposite quadrant after being reflected first over the y-axis and then the x-axis.

To summarize:

  • A point in Quadrant I (positive x, positive y) ends up in Quadrant III (negative x, negative y).
  • A point in Quadrant II (negative x, positive y) ends up in Quadrant IV (negative x, negative y).
  • A point in Quadrant III (negative x, negative y) ends up in Quadrant I (positive x, positive y).
  • A point in Quadrant IV (positive x, negative y) ends up in Quadrant II (negative x, positive y).

Thus, the final quadrant after both reflections can be determined by the original position of triangle ΔLOW.

If you identify the original location of triangle ΔLOW, it will be reflected across the y-axis and x-axis leading to the answer being the quadrant opposite to its original.

So if you can identify that original location (let's assume a specific quadrant), you can directly answer. If ΔLOW was originally in Quadrant I, for example, it will end up in Quadrant III after the two reflections.

Without the actual coordinates or a specific placement of triangle ΔLOW provided in the question, I can't definitively state which quadrant it will end up in. If you have access to the specific coordinates of points L, O, and W, you can determine their original quadrant and thus find the final quadrant after the reflections.