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 yy-coordinate of each point is negated while the xx-coordinate remains unchanged. This transformation is represented algebraically as:

(x,y)(x,y)(x, y) \to (x, -y)

Correct Answer:

B. (x, y) → (x, -y)


Would you like further details or clarification on this transformation?

Related Questions:

  1. How would the algebraic representation differ for a reflection across the y-axis?
  2. What happens to the coordinates if the triangle is reflected across the line y=xy = x?
  3. How would you write the rule for translating the triangle 3 units up and 2 units left?
  4. How can you verify that a reflection was performed correctly using coordinates?
  5. What changes would occur to triangle PQRPQR if reflected across the line y=xy = -x?

Tip:

For reflections, remember that the axis being reflected across determines which coordinate changes sign. The xx-axis affects yy, and the yy-axis affects xx.

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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