Answer:
To graph the image of the triangle after the transformation, we first need to have the coordinates of the vertices of the original triangle. Once we have those coordinates, we can apply the transformation to each vertex to obtain the coordinates of the corresponding vertex in the transformed image. Then, we can plot the three transformed vertices to obtain the image of the triangle.
Let's say the original triangle has vertices A, B, and C with coordinates A(x1, y1), B(x2, y2), and C(x3, y3), respectively.
To obtain the transformed coordinates of A, we apply the transformation rule (x, y) → (x - 1, y + 5) to the coordinates of A:
A' = (x1 - 1, y1 + 5)
Similarly, we can obtain the transformed coordinates of B and C:
B' = (x2 - 1, y2 + 5)
C' = (x3 - 1, y3 + 5)
Now that we have the transformed coordinates of the three vertices, we can plot them to obtain the image of the triangle.
Here's an example:
Suppose the original triangle has vertices A(2, 4), B(5, 6), and C(7, 3). Applying the transformation rule (x, y) → (x - 1, y + 5) to each vertex gives us:
A' = (2 - 1, 4 + 5) = (1, 9)
B' = (5 - 1, 6 + 5) = (4, 11)
C' = (7 - 1, 3 + 5) = (6, 8)
Plotting these three points gives us the image of the triangle after the transformation:
Before transformation:
B (5, 6)
/ \
/ \
A (2, 4) C (7, 3)
After transformation:
B' (4, 11)
/ \
/ \
A' (1, 9) C' (6, 8)
Here's what the image of the transformed triangle would look like on a graph:
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C' | B'
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---------|--------
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A' |
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