How could you determine the coordinates of the vertices of a translated image without using a graph?
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To determine the coordinates of the vertices of a translated image without using a graph, you would need to know the translation vector and the original coordinates of the vertices.
Here are the steps to follow:
1. Identify the translation vector: This vector represents the distance and direction of the translation. It has two components: the horizontal component (represented by the letter "a") and the vertical component (represented by the letter "b"). For example, if the translation vector is (3, -2), it means that the image has been moved three units to the right and two units down.
2. Find the original coordinates of the vertices: Each vertex of the original image has a set of coordinates (x, y). You can locate these points using any method, such as by measuring or using coordinates given in the problem.
3. Apply the translation vector to each vertex: To get the new coordinates of each vertex, add the horizontal component (a) of the translation vector to the original x-coordinate, and add the vertical component (b) of the translation vector to the original y-coordinate.
New_x = Original_x + a
New_y = Original_y + b
4. Repeat step 3 for each vertex: Apply the translation vector to each original vertex to find the new coordinates. This will give you the coordinates of the translated image.
For example, let's say you have a rectangle with the following original coordinates:
A(2, 3), B(5, 3), C(5, 6), D(2, 6)
If the translation vector is (3, -2), you would apply this vector to each original vertex:
A' = (2 + 3, 3 - 2) = (5, 1)
B' = (5 + 3, 3 - 2) = (8, 1)
C' = (5 + 3, 6 - 2) = (8, 4)
D' = (2 + 3, 6 - 2) = (5, 4)
Therefore, the coordinates of the translated image would be A'(5, 1), B'(8, 1), C'(8, 4), and D'(5, 4).
You would have to know the rule of the translation.
e.g.
(x,y) -----> (x+2, y-3)
and then do and check the arithmetic.