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Use the image to answer the question. 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 IV Quadrant IV Quadrant I Quadrant I Quadrant II Quadrant II Quadrant III

3 answers

To determine the quadrant of triangle \( \Delta LOW \) after the two reflections, we can follow these steps:

  1. Reflect across the y-axis: When a point \((x, y)\) is reflected across the y-axis, its coordinates change to \((-x, y)\). This means that the x-coordinates change signs while the y-coordinates remain the same.

  2. Reflect across the x-axis: When a point \((-x, y)\) is then reflected across the x-axis, its coordinates change to \((-x, -y)\). This means that both the x-coordinates and y-coordinates change signs.

Considering that reflecting a point affects its quadrant as follows:

  • Quadrant I (x > 0, y > 0) reflects to Quadrant II (x < 0, y > 0) after reflecting across the y-axis, then to Quadrant III (x < 0, y < 0) after reflecting across the x-axis.
  • Quadrant II (x < 0, y > 0) reflects to Quadrant I after reflecting across the y-axis, then to Quadrant IV (x > 0, y < 0) after reflecting across the x-axis.
  • Quadrant III (x < 0, y < 0) reflects to Quadrant IV after reflecting across the y-axis, then to Quadrant I after reflecting across the x-axis.
  • Quadrant IV (x > 0, y < 0) reflects to Quadrant III after reflecting across the y-axis, then to Quadrant II after reflecting across the x-axis.

To specifically answer your question about the triangle \( \Delta LOW \) reflecting across the y-axis then across the x-axis, it will end up in Quadrant III.

Use the image to answer the question. ΔLOW→ΔL"O"W" looks like a translation. What two moves could replace the one translation? (1 point) Responses a counterclockwise rotation of 180 degrees a counterclockwise rotation of 180 degrees a reflection across parallel lines a reflection across parallel lines a reflection across perpendicular lines a reflection across perpendicular lines a reflection across intersecting lines

To determine what two moves could replace a translation to transform \( \Delta LOW \) into \( \Delta L"O"W" \), we can consider the properties of transformations in geometry.

  1. Translation moves every point of a shape the same distance in the same direction.

To replace a translation with two moves, the common approach is to use two reflections. Specifically:

  • Reflection across parallel lines: This would effectively move a shape from one position to another without changing its orientation.

If you reflect an object across one line and then reflect the result across another parallel line, you will effectively recreate the translation.

Therefore, the correct response that describes two moves that could replace the one translation is:

a reflection across parallel lines.

This means that you can replace the translation of \( \Delta LOW \) to obtain \( \Delta L"O"W" \) with two reflections across parallel lines.