4. If the rule (x, y) ¡ú (x + 3, y ¨C 3) is applied to the original triangle, give the coordinates of and draw the image. Show your work (show the computation) for calculating the coordinates of the resulting image. Label the vertices correctly.
To apply the rule (x, y) → (x + 3, y - 3) to the original triangle, we need to find the images of each vertex.
Let's assume the original triangle has vertices A, B, and C with coordinates (x₁, y₁), (x₂, y₂), and (x₃, y₃) respectively.
For vertex A, the image can be found by adding 3 to the x-coordinate and subtracting 3 from the y-coordinate. So the new coordinates of A, denoted as A', will be (x₁ + 3, y₁ - 3).
For vertex B, the image can be found similarly, resulting in coordinates (x₂ + 3, y₂ - 3). Let's denote this as B'.
Lastly, for vertex C, the rule is also applied, giving us the coordinates (x₃ + 3, y₃ - 3). We will represent this image as C'.
Now, we can plot the original triangle and its image, labeled with the respective vertices. Keep in mind that I can only provide the steps, but I can't generate the image visually.
1. Plot points A (x₁, y₁), B (x₂, y₂), and C (x₃, y₃) on a coordinate plane.
2. Plot the new points A' (x₁ + 3, y₁ - 3), B' (x₂ + 3, y₂ - 3), and C' (x₃ + 3, y₃ - 3) on the same coordinate plane.
3. Connect the points A, B, and C to form the original triangle, and connect A', B', and C' to form the image triangle.
The resulting image triangle will have vertices A', B', and C'.
To find the coordinates of the resulting image after applying the given rule to the original triangle, you can start by labeling the vertices of the original triangle. Let's assume the vertices are A, B, and C.
Next, you need to apply the rule (x, y) ¡ú (x + 3, y ¨C 3) to each vertex of the original triangle and compute the new coordinates.
Let's calculate the new coordinates step by step:
Vertex A: (x, y) ¡ú (x + 3, y ¨C 3)
Let's assume the original coordinates of A are (x₁, y₁).
Applying the rule to A, we have:
A' = (x₁ + 3, y₁ ¨C 3)
Vertex B: (x, y) ¡ú (x + 3, y ¨C 3)
Assume the original coordinates of B are (x₂, y₂).
Applying the rule to B, we have:
B' = (x₂ + 3, y₂ ¨C 3)
Vertex C: (x, y) ¡ú (x + 3, y ¨C 3)
Assume the original coordinates of C are (x₃, y₃).
Applying the rule to C, we have:
C' = (x₃ + 3, y₃ ¨C 3)
Now we have the new coordinates of the vertices A', B', and C'. You can plot these points on a graph to draw the image of the resulting triangle.
Remember to label the vertices correctly, and you can connect the points to form the image of the resulting triangle.