Solved Triangle Transformations Worksheet

Hello! I am Acemy. I have analyzed your worksheet. It covers geometric transformations: translations (sliding), reflections (flipping), and rotations (turning).

Based on your image, here are the step-by-step solutions for your worksheet.

Answer

The problems involve identifying coordinates and describing how shapes move on a coordinate plane.

Explanation

1. Problem 1: Analyzing the Sequence The coordinates move from $(3,2), (5,2), (3,5)$ to $(-3,2), (-5,2), (-3,5)$, which is a reflection across the $y$-axis. Then, they move to $(-2,3), (-5,3), (-2,5)$, which is a shift.

   • First, $\Delta ABC$ was reflected across the $y$-axis to become $\Delta A'B'C'$.
   • Then, $\Delta A'B'C'$ was translated $1$ unit right and $1$ unit up to become $\Delta A''B''C''$.

2. Problem 2: Describing the Transformation Looking at the grid, the triangle $\Delta LJK$ is reflected over the $x$-axis to reach the lower quadrant, then it is translated.

   • First, $\Delta LJK$ was reflected over the $x$-axis to become $\Delta L'J'K'$.
   • Then, $\Delta L'J'K'$ was translated $4$ units to the right to become $\Delta L''J''K''$.

3. Problem 3: Multiple Choice Selection Comparing the positions, triangle $A$ at $(4, -4)$ is translated to $A'$ at $(4, 4)$, then reflected to $A''$ at $(-4, 4)$.

   • The correct sentences are b (A was translated) and d (Then $A'$ was reflected).

4. Problem 4: Translation Blanks Comparing point $A$ at $(1, 2)$ to $A'$ at $(-1, -2)$:

   • The $x$-coordinate changes from $1$ to $-1$ (a change of $-2$, or $2$ units left).
   • The $y$-coordinate changes from $2$ to $-2$ (a change of $-4$, or $4$ units down).
   • The answer is: A was translated 4 units down and 2 units left.

5. Problem 5: Error Analysis If you reflect $\Delta ABC$ ($x=3$) across the $y$-axis, it lands at $x=-3$. If you then reflect it across the $x$-axis to get the final position of $\Delta A'B'C'$, it matches the points shown.

   • I agree with Mr. Alvarez. A reflection across the $y$-axis followed by a reflection across the $x$-axis (which functions like a 180-degree rotation) correctly maps the triangle to the location of $\Delta A'B'C'$. Ms. Milano's translation method does not account for the change in the triangle's orientation (the flip).

Final Answer

For the Error Analysis in question 5, the correct choice is: $\boxed{\text{Mr. Alvarez}}$

Common Mistakes

• Directional confusion in translations: Always check if the coordinate is increasing or decreasing. Moving "left" means the $x$-value decreases, and "down" means the $y$-value decreases.
• Ignoring orientation in reflections: Remember that a reflection flips the shape. If the original triangle has point $C$ to the right of $B$, but the new triangle has $C$ to the left of $B$, a reflection must have occurred!