Podcast
Questions and Answers
What is the rule for the reflection of LMN?
What is the rule for the reflection of LMN?
ry-axis(x, y) → (-x, y)
What is the rule for the reflection of ABCD?
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?
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)?
Which figure represents the image of trapezoid LMNP after reflection using the rule ry-axis(x, y) → (-x, y)?
Which relationships hold true when reflecting ΔABC across the line of reflection PT?
Which relationships hold true when reflecting ΔABC across the line of reflection PT?
What line of reflection maps point K to point K' at (-5, 2)?
What line of reflection maps point K to point K' at (-5, 2)?
What line of reflection maps point L to point L' at (-2, 3)?
What line of reflection maps point L to point L' at (-2, 3)?
Which reflection creates an image of ΔRST with a vertex at (2, -3)?
Which reflection creates an image of ΔRST with a vertex at (2, -3)?
Which statements are true if figure DEFG is reflected across the x-axis? Check all that apply.
Which statements are true if figure DEFG is reflected across the x-axis? Check all that apply.
In which quadrant is point P' located after point P(-4, -7) is reflected across the x-axis?
In which quadrant is point P' located after point P(-4, -7) is reflected across the x-axis?
What are the coordinates of the pre-image of E' after figure ABCDE was reflected across the line y = x?
What are the coordinates of the pre-image of E' after figure ABCDE was reflected across the line y = x?
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)?
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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