Math Problem Statement
Tony graphs triangle PQR and reflects it across the x -axis to create triangle P′Q′R′ .
Which algebraic representation describes Tony’s reflection of PQR ? A.(x,y)→(x,y−6)
B.(x,y)→(x,−y)
C.(x,y)→(−x,y)
D.(x,y)→(−y,x)
Solution
To reflect a triangle across the x-axis, the -coordinate of each point is negated while the -coordinate remains unchanged. This transformation is represented algebraically as:
Correct Answer:
B. (x, y) → (x, -y)
Would you like further details or clarification on this transformation?
Related Questions:
- How would the algebraic representation differ for a reflection across the y-axis?
- What happens to the coordinates if the triangle is reflected across the line ?
- How would you write the rule for translating the triangle 3 units up and 2 units left?
- How can you verify that a reflection was performed correctly using coordinates?
- What changes would occur to triangle if reflected across the line ?
Tip:
For reflections, remember that the axis being reflected across determines which coordinate changes sign. The -axis affects , and the -axis affects .
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Math Problem Analysis
Mathematical Concepts
Geometry
Transformations
Reflections
Formulas
Reflection across the x-axis: (x, y) → (x, -y)
Theorems
Reflection theorem in coordinate geometry
Suitable Grade Level
Grades 8-10