Math Problem Statement
Graph triangle RST with vertices R(4, 1), S(7, 3), and T(6, 4) and its image after the glide reflection. Also, determine the number of lines of symmetry for given figures.
Solution
Let's solve the questions based on the provided image.
Question 17: Graph and Glide Reflection
Given:
- Vertices of ΔRST:
- Translation:
- Reflection: Reflection across the -axis.
-
Translation: Translate each vertex of by reducing the -coordinate by 1:
-
Reflection in the -axis: Reflect each over the -axis:
Final vertices of the reflected triangle are:
- , , .
Question 21: Number of Lines of Symmetry for the Trapezoid
- The trapezoid shown is isosceles (sides are symmetric about the vertical axis).
- Number of Lines of Symmetry: 1 (the vertical line passing through the midpoint of the top and bottom sides).
Question 22: Number of Lines of Symmetry for the Cross Shape
- The cross shape is symmetric both vertically and horizontally and along both diagonals.
- Number of Lines of Symmetry: 4.
Would you like further details, graphs, or visual explanations? Let me know!
Here are 5 related questions to expand your understanding:
- How do you graph transformations like reflections and translations on a coordinate plane?
- Can every shape have a line of symmetry? Why or why not?
- How do diagonal lines of symmetry differ from vertical or horizontal ones?
- What are the effects of combining transformations, such as translation followed by reflection?
- How do you verify if a figure has a specific number of lines of symmetry?
Tip: Always perform transformations step-by-step to avoid errors in composite operations!
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Math Problem Analysis
Mathematical Concepts
Transformations
Glide Reflection
Symmetry
Formulas
Translation: (x, y) → (x, y - 1)
Reflection across y-axis: (x, y) → (-x, y)
Theorems
Reflection Theorem
Properties of Symmetry
Suitable Grade Level
Grades 8-10