Geometry Reflections Flashcards

Questions and Answers

What is the rule for the reflection?

rx-axis(x, y) → (x, -y) (correct)

ry-axis(x, y) → (x, -y) (correct)

rx-axis(x, y) → (-x, y) (correct)

ry-axis(x, y) → (-x, y) (correct)

Which statements must be true about the reflection of ΔXYZ across ? Select three options.

Statement a

Statement b (correct)

Statement d (correct)

Statement c

Statement e (correct)

For ΔA'B'C' constructed using ΔABC and line segment EH, which statements must be true? Select three options.

Statement d (correct)

Statement a (correct)

Statement b

Statement e

Statement c (correct)

What is the length of RZ after the reflection across parallelogram PQRS?

6 Signup and view all the answers

What is the pre-image of vertex A' if the image shown on the graph was created by a reflection across the y-axis?

(-6, 8) Signup and view all the answers

Which statements must be true about the image of ΔMNP after a reflection across? Select three options.

The line segments connecting corresponding vertices will all be parallel to each other. Signup and view all the answers

What is true about point F after the reflection of ΔABC?

Statement a Signup and view all the answers

What is the rule for the reflection across the line ry=x?

ry=x(x, y) → (y, x) Signup and view all the answers

What are the coordinates of the image of vertex G after a reflection across the line y = x?

(-5, 4) Signup and view all the answers

Which triangle must be a right triangle and why after the reflection of ΔABC?

ΔBGC is right because CC'. Signup and view all the answers

Study Notes

Reflection Rules

Reflection across the x-axis transforms coordinates as follows: (x, y) → (x, -y).
Reflection across the y-axis transforms coordinates: (x, y) → (-x, y).
Reflection across the line y = x swaps the coordinates: (x, y) → (y, x).
Reflection across the line y = -x also reverses coordinates but changes their signs: (x, y) → (-y, -x).

Statements About Reflection

For a triangle ΔXYZ reflected, only specific statements hold true regarding congruency, orientation, and relationships between vertices.
True statements relate to angles and lengths remaining constant after reflection.

Line of Reflection

When constructing ΔA'B'C' from ΔABC using line segment EH, certain conditions must be satisfied for EH to be the line of reflection.
Essential truths revolve around distance preservation and point relationships.

Length After Reflection

If the length of the segment has a specific value, after a reflection, lengths may remain unchanged or have a specific correlation based on reflective properties.

Pre-image Coordinates

For vertex transformations after reflection, specific coordinates can determine the pre-image; critical to note are signs and positions in relation to reflection lines.

Triangle Properties After Reflection

The reflected image of a triangle maintains congruency but may change orientation based on the line of reflection.
Perpendicular bisectors connect corresponding vertices, forming distinct geometric properties post-reflection.

Identifying Right Triangles

Among reflected triangles, distinctions can be made about which must necessarily be right triangles based on relationships with reflection lines and the properties of triangles.

Coordinate Transformations

Identifying image coordinates after reflection involves understanding the geometric principles underlying each specific reflection line, such as y = x for the swapping of x and y values, with sign adjustments based on the specifics of the line in question.

Description

Test your understanding of reflections in geometry with these flashcards. Learn the rules for reflecting points across the x-axis and y-axis, and evaluate the properties of reflected triangles. Ideal for students preparing for geometry assessments!