Question
Congruent Figures Practice
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Question
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An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 10 to 10 in increments of 1. Three triangles are plotted on the graph. The triangle upper A upper B upper C has its vertices marked with closed points at upper A left parenthesis 2 comma negative 2 right parenthesis, upper B left parenthesis 2 comma negative 4 right parenthesis, and upper C left parenthesis 5 comma negative 4 right parenthesis. The second triangle, placed in the second quadrant, has its vertices marked with closed points at left parenthesis negative 3 comma 6 right parenthesis, left parenthesis negative 5 comma 6 right parenthesis, and left parenthesis negative 5 comma 3 right parenthesis. The third triangle, placed in the third quadrant, has its vertices marked with closed points at left parenthesis negative 2 comma negative 2 right parenthesis, left parenthesis negative 4 comma negative 2 right parenthesis, and left parenthesis negative 4 comma negative 5 right parenthesis. An arrow goes from the point left parenthesis negative 2 comma negative 2 right parenthesis to left parenthesis negative 3 comma 6 right parenthesis; an arrow goes from the point left parenthesis negative 4 comma negative 2 right parenthesis to left parenthesis negative 5 comma 6 right parenthesis; an arrow goes from left parenthesis negative 4 comma negative 5 right parenthesis to left parenthesis negative 5 comma 3 right parenthesis.
What sequence of transformations is depicted in the figure, proving the congruence of the triangles?
(1 point)
rotation of
degrees clockwise about the origin, then translation of (
)
Remaining Attempts : 3
Complete this assessment to review what you've learned. It will not count toward your grade.
5 of 55 of 5 Items
View previous attempt
Question
Use the image to answer the question.
An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 10 to 10 in increments of 1. Three triangles are plotted on the graph. The triangle upper A upper B upper C has its vertices marked with closed points at upper A left parenthesis 2 comma negative 2 right parenthesis, upper B left parenthesis 2 comma negative 4 right parenthesis, and upper C left parenthesis 5 comma negative 4 right parenthesis. The second triangle, placed in the second quadrant, has its vertices marked with closed points at left parenthesis negative 3 comma 6 right parenthesis, left parenthesis negative 5 comma 6 right parenthesis, and left parenthesis negative 5 comma 3 right parenthesis. The third triangle, placed in the third quadrant, has its vertices marked with closed points at left parenthesis negative 2 comma negative 2 right parenthesis, left parenthesis negative 4 comma negative 2 right parenthesis, and left parenthesis negative 4 comma negative 5 right parenthesis. An arrow goes from the point left parenthesis negative 2 comma negative 2 right parenthesis to left parenthesis negative 3 comma 6 right parenthesis; an arrow goes from the point left parenthesis negative 4 comma negative 2 right parenthesis to left parenthesis negative 5 comma 6 right parenthesis; an arrow goes from left parenthesis negative 4 comma negative 5 right parenthesis to left parenthesis negative 5 comma 3 right parenthesis.
What sequence of transformations is depicted in the figure, proving the congruence of the triangles?
(1 point)
rotation of
degrees clockwise about the origin, then translation of (
)
Remaining Attempts : 3
Answers
GPT-4o mini
To determine the sequence of transformations that shows the congruence of the triangles, we can analyze the movements described in your question.
1. **Rotation**: The first triangle, A(2, -2), B(2, -4), C(5, -4) appears to be rotated into the position of the second triangle, which has vertices (-3, 6), (-5, 6), and (-5, 3). Observing the coordinates suggests that the first triangle has been rotated counter-clockwise by 90 degrees about the origin. After a 90-degree rotation, point A(2, -2) moves to approximately (2, 2), point B(2, -4) moves to (4, 2), and point C(5, -4) goes to (4, -5).
2. **Translation**: The triangles’ vertices then undergo translation. The rotation positions the first triangle near where the second triangle is located, but the triangles are not yet congruent until we translate the vertices.
To summarize:
- The first transformation is a **90-degree counter-clockwise rotation** around the origin.
- The specific translation after this rotation can be determined by looking at the specific movements of the points to their corresponding positions in the resulting triangle. For example, the point (2, -2) that rotated to (2, 2) then would need to move to (-3, 6), which outlines a translation of (-5, 4).
Thus, the complete transformation sequence demonstrating congruence is:
- A **90 degrees counter-clockwise rotation** about the origin, followed by a **translation of (-5, 4)**.
So, you can input your answer in this format:
**(1 point) rotation of 90 degrees counter-clockwise about the origin, then translation of (-5, 4)**.
Please confirm your final answer according to the answer format required in your assessment.
1. **Rotation**: The first triangle, A(2, -2), B(2, -4), C(5, -4) appears to be rotated into the position of the second triangle, which has vertices (-3, 6), (-5, 6), and (-5, 3). Observing the coordinates suggests that the first triangle has been rotated counter-clockwise by 90 degrees about the origin. After a 90-degree rotation, point A(2, -2) moves to approximately (2, 2), point B(2, -4) moves to (4, 2), and point C(5, -4) goes to (4, -5).
2. **Translation**: The triangles’ vertices then undergo translation. The rotation positions the first triangle near where the second triangle is located, but the triangles are not yet congruent until we translate the vertices.
To summarize:
- The first transformation is a **90-degree counter-clockwise rotation** around the origin.
- The specific translation after this rotation can be determined by looking at the specific movements of the points to their corresponding positions in the resulting triangle. For example, the point (2, -2) that rotated to (2, 2) then would need to move to (-3, 6), which outlines a translation of (-5, 4).
Thus, the complete transformation sequence demonstrating congruence is:
- A **90 degrees counter-clockwise rotation** about the origin, followed by a **translation of (-5, 4)**.
So, you can input your answer in this format:
**(1 point) rotation of 90 degrees counter-clockwise about the origin, then translation of (-5, 4)**.
Please confirm your final answer according to the answer format required in your assessment.