Math Problem Statement
Solution
Let's go step by step through the transformations for point C.
-
Reflection across the x-axis:
- The original coordinates of point C are .
- 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 (since the y-coordinate is 0, the reflection doesn't change it).
-
Translation 5 units to the left:
- Translating left by 5 units means subtracting 5 from the x-coordinate.
- The x-coordinate of C' is , so:
- The y-coordinate remains the same (0).
Thus, the coordinates of C'' after both transformations are . 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:
- How do transformations affect other points in the triangle?
- What happens when you reflect over the y-axis instead?
- How would you translate a point 5 units right instead of left?
- What if the reflection was over the line ?
- 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
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