Question

name: deionta mcduttie date: sequences of transformations - a.c.e.s. writing practice triangle abc and triangle abc are shown on the right. a student says that they can reflect triangle abc across the x - axis and then translate it 10 units to the right in order to create abc. do you agree with this student? justify your reasoning in the space below. how would we answer a question like this on anet? answer: write one sentence explaining if you agree or not. cite: write one sentence explaining what strategy you used to determine your answer. explain: write 1 sentence elaborating on what you would do in order to perform this transformation correctly. summarize: write one sentence restating your answer!

Explanation:

When reflecting a shape across the \(x -\)axis, the \(y -\)coordinates of its vertices change sign (\((x,y)\to(x, - y)\)). Then, translating 10 units to the right changes the \(x -\)coordinates (\((x,y)\to(x + 10,y)\)). But in the given case, after reflection across the \(x -\)axis and translation 10 units right, there is also a vertical translation (change in \(y -\)coordinate other than just the reflection - induced sign change) needed. The student's transformation only accounts for reflection and horizontal translation, missing the vertical adjustment.

Answer:

No, I do not agree.
Cite: Analyzed orientation and position of triangles after transformations.
Explain: First, reflect Triangle \(ABC\) across the \(x -\)axis, then translate 10 units right and 1 unit down.
Summarize: Student’s transformation lacks necessary vertical translation.