Select the correct answer from each drop-down menu.
Consider figures 1 and 2 on the coordinate plane.
Graph shows two triangles plotted on a coordinate plane. Triangle 1 is at (5, 2), (5, 7), and (8, 5). Triangle 2 is at (minus 7, 2), (minus 5, 5), and (minus 2, 2).
Which sequence of transformations maps figure 1 onto figure 2?
Figure 1 is mapped onto figure 2 by a
rotation about the origin followed by a translation of
.
Figure 1 is mapped onto figure 2 by a rotation about the origin followed by a translation of (+3, 0).
Figure 1 is mapped onto figure 2 by a rotation about the origin followed by a translation of ____.
To determine the sequence of transformations, we need to analyze how the coordinates of the vertices change from figure 1 to figure 2.
Triangle 1 (- original coordinates):
Vertex 1: (5, 2)
Vertex 2: (5, 7)
Vertex 3: (8, 5)
Triangle 2 (- new coordinates):
Vertex 1: (-7, 2)
Vertex 2: (-5, 5)
Vertex 3: (-2, 2)
By comparing the coordinates, we can observe the following transformations:
1. There is a horizontal translation of 12 units to the left (negative x-axis direction) since the x-coordinates are decremented by 12 units from Triangle 1 to Triangle 2.
2. There is a vertical translation of 3 units downwards (negative y-axis direction) since the y-coordinates are decremented by 3 units from Triangle 1 to Triangle 2.
Thus, the sequence of transformations that maps figure 1 onto figure 2 is a rotation about the origin followed by a translation of 12 units to the left (negative x-axis direction) and 3 units downwards (negative y-axis direction).
To determine the sequence of transformations that maps figure 1 onto figure 2, let's analyze the given information.
1) Triangle 1: The vertices of triangle 1 are (5, 2), (5, 7), and (8, 5).
2) Triangle 2: The vertices of triangle 2 are (-7, 2), (-5, 5), and (-2, 2).
Since triangle 1 is mapped onto triangle 2, we need to find the rotation and translation applied to triangle 1 to obtain triangle 2.
1) Rotation: To determine the rotation, analyze the movement of each vertex.
- The vertex (5, 2) in triangle 1 is mapped to (-7, 2) in triangle 2. It has not moved vertically but has moved in the negative x-direction by 12 units.
- The vertex (5, 7) in triangle 1 is mapped to (-5, 5) in triangle 2. It has moved horizontally to the left by 10 units and vertically down by 2 units.
- The vertex (8, 5) in triangle 1 is mapped to (-2, 2) in triangle 2. It has moved horizontally to the left by 10 units and vertically up by 3 units.
Based on the movements of the vertices, we can see that triangle 1 has been rotated about the origin in a clockwise direction. Since the x-coordinates are decreasing by 12 units and the y-coordinates are changing, it indicates a rotation but doesn't specify the angle.
2) Translation: To determine the translation, analyze the movement of a common vertex after the rotation.
- The vertex (5, 7) in triangle 1 is mapped to (-5, 5) in triangle 2. It has moved horizontally to the left by 10 units and vertically down by 2 units.
From the above analysis, the sequence of transformations that maps figure 1 onto figure 2 is:
1) A clockwise rotation about the origin (angle unknown)
2) A translation to the left by 10 units and downwards by 2 units.
The complete answer would require specifying the angle of rotation, which is not provided in the given information.