Questions and Answers
What is the rule for the reflection of LMN?
ry-axis(x, y) → (-x, y)
What is the rule for the reflection of ABCD?
rx-axis(x, y) → (x, -y)
What are the coordinates of the image D' after reflecting point D(a, b) over the line y = x?
b, a
Which figure represents the image of trapezoid LMNP after reflection using the rule ry-axis(x, y) → (-x, y)?
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Which relationships hold true when reflecting ΔABC across the line of reflection PT?
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What line of reflection maps point K to point K' at (-5, 2)?
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What line of reflection maps point L to point L' at (-2, 3)?
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Which reflection creates an image of ΔRST with a vertex at (2, -3)?
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Which statements are true if figure DEFG is reflected across the x-axis? Check all that apply.
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In which quadrant is point P' located after point P(-4, -7) is reflected across the x-axis?
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What are the coordinates of the pre-image of E' after figure ABCDE was reflected across the line y = x?
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What are the coordinates of the pre-image if the image of a point is given by the rule ry = -x(x, y) → (-4, 9)?
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Study Notes
Reflection Rules
- Reflection across the y-axis follows the rule: (x, y) → (-x, y).
- Reflection across the x-axis follows the rule: (x, y) → (x, -y).
Coordinate Transformation
- For point D at coordinates (a, b), reflecting over the line y = x results in new coordinates D' being (b, a).
Geometry Reflection Examples
- Trapezoid LMNP reflected over the y-axis produces a new figure; in a given context, figure C is the resulting image.
- When reflecting triangle ΔABC across line PT, properties include: the segments C'Q = QC, PT is perpendicular to A'A, A'A is parallel to B'B, and angle m∠TRB is 90°.
Lines of Reflection
- To map point K to K' at (-5, 2), the line of reflection is the y-axis.
- To map point L to L' at (-2, 3), the line of reflection is y = -x.
Vertex Reflections
- Reflecting ΔRST across the line y = -x will position one vertex at (2, -3).
Effects of Reflection Across the x-axis
- After reflection across the x-axis, point D at coordinates (0, 4) becomes D' at (0, -4).
- Point E at (-2, 0) remains unchanged after reflection, resulting in E' at (-2, 0).
- The distance from G' to the x-axis post-reflection is 2 units.
Quadrant Location After Reflection
- Reflecting point P located at (-4, -7) across the x-axis results in P' being positioned in Quadrant II.
Pre-image Coordinates
- Reflecting figure ABCDE across the line y = x results in the pre-image of point E' being at coordinates (-2, 6).
- The pre-image of a point corresponding to the image (-4, 9) under the rule y = -x is found to be (-9, 4).
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Description
Test your knowledge on geometric reflections with these flashcards. Focus on the rules of reflection across the x-axis and y-axis, and apply these concepts to specific figures in the coordinate plane.
