How could you determine the coordinates of the vertices of a translated image without using a graph?
apply the transformation to the original coordinates.
google can provide many discussions and examples.
You would have to know what the translation is
e.g. suppose we have the translation (x,y) -----> (x+2,y-1)
and you had a triangle A(4,5), B(-2,9) and C(0,0)
then the translated triangle would be
A'(6,4) , B'(0,8) and C'(2,-1)
What do you notice about the ordered pairs of the original figure and the ordered pairs
of the rotation about the origin?
How could you determine the coordinates of the vertices of a translated image without using a graph?
no
To determine the coordinates of the vertices of a translated image without using a graph, you can follow these steps:
1. Identify the translation vector: Find the horizontal and vertical shift between the original shape and its translated image. This vector represents the direction and distance of the translation.
2. Locate a known vertex: Choose a vertex on the original shape that is easy to identify and has known coordinates. This will serve as a reference point.
3. Apply the translation vector: Add or subtract the horizontal and vertical components of the translation vector to the coordinates of the known vertex. The result will give you the coordinates of the corresponding vertex on the translated shape.
4. Repeat for all other vertices: Use the same translation vector to find the coordinates of the remaining vertices by applying the translation to each vertex.
Example:
Let's say we have a triangle ABC with coordinates A(2, 3), B(5, 2), and C(4, 6). We want to determine the coordinates of the vertices of its translated image.
1. Suppose we know that the translation vector is (3, -1). This means the image is shifted 3 units to the right and 1 unit downward.
2. Let's choose point A(2, 3) as the reference point.
3. We apply the translation vector to A:
New_x = 2 + 3 = 5
New_y = 3 - 1 = 2
Therefore, the coordinates of the translated point A' are (5, 2).
4. Repeat for B and C using the same translation vector:
B' = (5 + 3, 2 - 1) = (8, 1)
C' = (4 + 3, 6 - 1) = (7, 5)
So, the translated triangle has vertices A'(5, 2), B'(8, 1), and C'(7, 5).
By following these steps, you can determine the coordinates of the vertices of a translated image without relying on a graph.