Math Problem Statement

Triangle ABC is translated 3 points left and 8 points up. The mapped triangle has vertices A'(1, -5), B'(1, -7), and C'(7, -6). Find the coordinates of point C.

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 A(1,5)A'(1, -5), B(1,7)B'(1, -7), and C(7,6)C'(7, -6). We are tasked with finding the original coordinates of point CC.

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 CC (denoted as C(x,y)C(x, y)), we need to reverse the translation:

  • For the x-coordinate: Add 3 to C(7,6)C'(7, -6)'s x-coordinate: 7+3=107 + 3 = 10.
  • For the y-coordinate: Subtract 8 from C(7,6)C'(7, -6)'s y-coordinate: 68=14-6 - 8 = -14.

Thus, the original coordinates of point CC are (10,14)(10, -14).

Let me know if you'd like more details or if you have any questions!

Here are 5 related questions:

  1. What would be the coordinates of point AA before translation?
  2. What is the original location of point BB?
  3. How can you generalize translation for other transformations?
  4. How would a reflection across the x-axis change the coordinates of triangle ABC?
  5. 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