which two transformations could have been used to create figure 2?

drag and drop the correct transformations into the boxes.

first, figure 1 was

then, it was to create figure 2.

options:
- translated down 7 units
- reflected across the $x$-axis
- rotated $90^\circ$ clockwise around the origin
- rotated $90^\circ$ counterclockwise around the origin

Question

which two transformations could have been used to create figure 2?

drag and drop the correct transformations into the boxes.

first, figure 1 was

then, it was   to create figure 2.

options:
- translated down 7 units
- reflected across the $x$-axis
- rotated $90^\circ$ clockwise around the origin
- rotated $90^\circ$ counterclockwise around the origin

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Geometric Transformations", "Coordinate Rules for Rotations", "Reflections in Coordinate Plane" ], "current_concepts": [ "Geometric Transformations", "Coordinate Rules for Rotations", "Reflections in Coordinate Plane" ] } ## Identify key vertices of Figure 1 and Figure 2 $$ \begin{aligned} &\text{Figure 1 vertices: } A(-5, 2), B(-3, 2), C(-2, 5), D(-4, 5), E(-4.5, 3.5) \ &\text{Figure 2 vertices: } A'(2, -5), B'(2, -3), C'(5, -2), D'(5, -4), E'(3.5, -4.5) \end{aligned} $$ ## Test transformation sequences $$ \begin{aligned} &\text{Let } (x, y) \text{ be a point on Figure 1.} \ &\text{If reflected across the } x\text{-axis: } (x, y) \to (x, -y) \ &\text{Applying to } A(-5, 2) \to A_1(-5, -2) \ &\text{If then rotated } 90^\circ \text{ counterclockwise around the origin: } (x_1, y_1) \to (-y_1, x_1) \ &\text{Applying to } A_1(-5, -2) \to A'(-(-2), -5) = (2, -5) \ &\text{Applying to } C(-2, 5) \to C_1(-2, -5) \to C'(-(-5), -2) = (5, -2) \end{aligned} $$ ## Verify matching with options $$ \begin{aligned} &\text{First transformation: "reflected across the } x\text{-axis"} \ &\text{Second transformation: "rotated } 90^\circ \text{ counterclockwise around the origin"} \end{aligned} $$ First, figure 1 was reflected across the $x$-axis Then, it was rotated $90^\circ$ counterclockwise around the origin to create figure 2. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Geometric Transformations" ] }

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QUESTION IMAGE

Question

Explanation:

Identify key vertices of Figure 1 and Figure 2

Test transformation sequences

Verify matching with options

Answer: