Math Problem Statement
Solution
We are given the translated vertices of triangle ABC after a translation of 3 units left and 8 units up. The translated triangle has vertices , , and . We are tasked with finding the original coordinates of point .
Translation Information:
- Moving left by 3 points means subtracting 3 from the x-coordinates.
- Moving up by 8 points means adding 8 to the y-coordinates.
Reversing the Translation:
To find the original coordinates of point (denoted as ), we need to reverse the translation:
- For the x-coordinate: Add 3 to 's x-coordinate: .
- For the y-coordinate: Subtract 8 from 's y-coordinate: .
Thus, the original coordinates of point are .
Let me know if you'd like more details or if you have any questions!
Here are 5 related questions:
- What would be the coordinates of point before translation?
- What is the original location of point ?
- How can you generalize translation for other transformations?
- How would a reflection across the x-axis change the coordinates of triangle ABC?
- How would a dilation centered at the origin affect the triangle's vertices?
Tip: When reversing a transformation, apply the opposite operation to each coordinate.
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Math Problem Analysis
Mathematical Concepts
Geometry
Coordinate Geometry
Translations
Formulas
Translation Formula: (x, y) -> (x - a, y + b)
Theorems
Transformation Theorems
Suitable Grade Level
Grades 8-10
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