To solve this problem, we need to determine the geometric transformation that moves the first triangle (let's call it Triangle A) to the position of the second triangle (Triangle B).
Step 1: Identify the coordinates of the vertices.
Let's look at the grid to find the $(x, y)$ coordinates for the corners of each triangle.
*
Triangle A (Top Purple Triangle):
* Top vertex: $(0, 3)$
* Bottom-left vertex: $(-1, 2)$
* Bottom-right vertex: $(1, 2)$
*
Triangle B (Right Purple Triangle):
* Rightmost vertex: $(3, 0)$
* Top-left vertex: $(2, 1)$
* Bottom-left vertex: $(2, -1)$
Step 2: Analyze the change in orientation.
Triangle A is pointing upwards. Triangle B is pointing to the right. This suggests a rotation. Specifically, turning an "up" arrow to point "right" is a
90-degree clockwise rotation.
Step 3: Test the rotation rule.
The rule for rotating a point 90 degrees clockwise around the origin $(0,0)$ is:
$$(x, y) \rightarrow (y, -x)$$
Let's apply this rule to the vertices of Triangle A to see if they match Triangle B.
*
Vertex 1: Top of Triangle A is $(0, 3)$.
* Apply rule: $(3, -0) \rightarrow (3, 0)$.
* Does this match a vertex on Triangle B? Yes, it matches the rightmost vertex $(3, 0)$.
*
Vertex 2: Bottom-right of Triangle A is $(1, 2)$.
* Apply rule: $(2, -1) \rightarrow (2, -1)$.
* Does this match a vertex on Triangle B? Yes, it matches the bottom-left vertex $(2, -1)$.
*
Vertex 3: Bottom-left of Triangle A is $(-1, 2)$.
* Apply rule: $(2, -(-1)) \rightarrow (2, 1)$.
* Does this match a vertex on Triangle B? Yes, it matches the top-left vertex $(2, 1)$.
Conclusion:
Since applying the 90-degree clockwise rotation rule to every vertex of the first triangle results in the exact coordinates of the second triangle, the transformation is a rotation of 90 degrees clockwise about the origin.
Final Answer:
Rotation 90° clockwise about the origin
Parent Tip: Review the logic above to help your child master the concept of rotations translations reflections worksheet.
