The figure shows two triangles on the coordinate grid:
A coordinate grid is shown from positive 6 to negative 6 on the x-axis and from positive 6 to negative 6 on the y-axis. A triangle ABC is shown with vertex A on ordered pair negative 4, negative 1, vertex B on ordered pair negative 3, negative 1 and vertex C on ordered pair negative 4, negative 4. Another triangle A prime B prime C prime is shown with vertex A prime on ordered pair negative 1, 1, vertex B prime on ordered pair negative 2, 1, and vertex C prime on ordered pair negative 1, 4.
What set of transformations is performed on triangle ABC to form triangle A'B'C'?
A translation 5 units up, followed by a 270-degree counterclockwise rotation about the origin
A 270-degree counterclockwise rotation about the origin, followed by a translation 5 units up. I think its this one.
A 180-degree counterclockwise rotation about the origin, followed by a translation 5 units to the right
A translation 5 units to the right, followed by a 180-degree counterclockwise rotation about the origin
the answer is --> A translation 5 units to the right, followed by a 180-degree counterclockwise rotation about the origin
:)
The correct set of transformations performed on triangle ABC to form triangle A'B'C' is:
A translation 5 units up, followed by a 270-degree counterclockwise rotation about the origin.
To determine the set of transformations performed on triangle ABC to form triangle A'B'C', we need to analyze the changes in the coordinates of the vertices.
Triangle ABC is initially located at (-4, -1), (-3, -1), and (-4, -4).
Triangle A'B'C' is located at (-1, 1), (-2, 1), and (-1, 4).
Let's go through the answer choices and see which one matches the given transformations:
1. A translation 5 units up, followed by a 270-degree counterclockwise rotation about the origin:
If we perform a translation 5 units up on triangle ABC, the new coordinates would be (-4, 4), (-3, 4), and (-4, -1). Then, if we rotate it 270 degrees counterclockwise about the origin, the new coordinates would become (4, -4), (4, -3), and (1, -4). As we can see, these coordinates are different from those of triangle A'B'C', so this choice is incorrect.
2. A 270-degree counterclockwise rotation about the origin, followed by a translation 5 units up:
If we rotate triangle ABC 270 degrees counterclockwise, the new coordinates would be (1, -4), (1, -3), and (4, -4). Then, if we perform a translation 5 units up, the new coordinates would become (1, 1), (1, 2), and (4, 1). These coordinates match those of triangle A'B'C', so this choice is correct.
3. A 180-degree counterclockwise rotation about the origin, followed by a translation 5 units to the right:
If we rotate triangle ABC 180 degrees counterclockwise, the new coordinates would be (4, 1), (3, 1), and (4, 4). Then, if we perform a translation 5 units to the right, the new coordinates would become (9, 1), (8, 1), and (9, 4). As we can see, these coordinates are different from those of triangle A'B'C', so this choice is incorrect.
4. A translation 5 units to the right, followed by a 180-degree counterclockwise rotation about the origin:
If we perform a translation 5 units to the right on triangle ABC, the new coordinates would be (1, -1), (2, -1), and (1, -4). Then, if we rotate it 180 degrees counterclockwise about the origin, the new coordinates would become (-1, 1), (-2, 1), and (-1, 4). As we can see, these coordinates match those of triangle A'B'C', so this choice is also correct.
Therefore, the correct answer is option 2: A 270-degree counterclockwise rotation about the origin, followed by a translation 5 units up.
geez, you have a problem with using actual math notation? Try saying
A triangle ABC is shown with vertices
A = (-4,-1)
B = (-3,-1)
C = (-4,-4)
Another triangle A'B'C' shown with vertices
A' = (-1,1)
B' = (-2,1)
C' = (-1,4)
Now, isn't that a lot easier to handle?
Clearly it was rotated 180°
so, what else?