Math Problem Statement

Perform the given sequence of transformations: Reflect across the x-axis. Translate 5 units left. What are the coordinates of C''?

Solution

Let's go step by step through the transformations for point C.

  1. Reflection across the x-axis:

    • The original coordinates of point C are (3,0)(-3, 0).
    • When reflecting across the x-axis, the y-coordinate changes its sign, but the x-coordinate remains the same.
    • So, after reflecting across the x-axis, the new coordinates of point C' will be (3,0)(-3, 0) (since the y-coordinate is 0, the reflection doesn't change it).
  2. Translation 5 units to the left:

    • Translating left by 5 units means subtracting 5 from the x-coordinate.
    • The x-coordinate of C' is 3-3, so: 35=8-3 - 5 = -8
    • The y-coordinate remains the same (0).

Thus, the coordinates of C'' after both transformations are (8,0)(-8, 0). However, this isn't listed as one of the options.

Looking back at the options, it seems like there might be a mistake in the problem's options, or another detail might need clarification. Would you like to ask for clarification or discuss further?


Here are 5 questions to extend understanding:

  1. How do transformations affect other points in the triangle?
  2. What happens when you reflect over the y-axis instead?
  3. How would you translate a point 5 units right instead of left?
  4. What if the reflection was over the line y=xy = x?
  5. How would the transformation change if the translation was vertical?

Tip: Always double-check transformations visually by plotting the points on graph paper!

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Transformations

Formulas

Reflection across x-axis: (x, y) -> (x, -y)
Translation left by n units: (x, y) -> (x - n, y)

Theorems

Transformation Theorem
Reflection and Translation

Suitable Grade Level

Grades 6-8