if a triangle with vertices (4,3), (3,7), and (7,5) is translated to the right 4 units and down 2 units, what are the vertices of the translated figure?
To translate a figure to the right 4 units, we add 4 to the x-coordinates of each vertex. To translate it down 2 units, we subtract 2 from the y-coordinates of each vertex.
The given triangle has vertices (4, 3), (3, 7), and (7, 5).
Translating the triangle to the right 4 units, we add 4 to the x-coordinates:
(4+4, 3) = (8, 3)
(3+4, 7) = (7, 7)
(7+4, 5) = (11, 5)
Now we translate the new triangle down 2 units by subtracting 2 from the y-coordinates:
(8, 3-2) = (8, 1)
(7, 7-2) = (7, 5)
(11, 5-2) = (11, 3)
Therefore, the vertices of the translated figure are (8, 1), (7, 5), and (11, 3).
what's the correct one
8,3 12,3 and 11,5
0,1 4,1 and 3,3
8,5 12,5 and 11,7
8,1 12,1 and 11,3
Apologies for the confusion. The correct vertices of the translated figure are (8, 1), (12, 1), and (11, 3).
which transformation(s) will result in a figure that has the same orientation as the original figure?
To obtain a figure with the same orientation as the original figure, we need to perform transformations that do not change the relative positioning of the vertices.
The possible transformations that result in a figure with the same orientation are:
1. Translation: This is the movement of the entire figure in a specific direction. To maintain the same orientation, the translation has to be linear, meaning we move the figure either up/down or left/right, without rotating or flipping it.
2. Reflection: This transformation mirrors the figure across a line (often a vertical or horizontal line). If the reflection line is such that it maintains the same orientation of the original figure, the orientation will be preserved.
3. Combination of translation and rotation: This involves both moving the figure and rotating it. If the rotation angle is such that it keeps the same orientation, the figure will have the same orientation as the original.
However, it is important to note that scaling (changing the size) or shearing (distorting the angles) will not maintain the same orientation of the original figure.