To graph triangle ABC and its dilation with a scale factor of 0.25, we first need to determine the new coordinates for each vertex after the dilation. The formula for the dilation of a point \((x, y)\) with respect to the origin is:
\[ (x', y') = (kx, ky) \]
where \(k\) is the scale factor. In this case, the scale factor \(k = 0.25\).
Step 1: Calculate the new coordinates after dilation
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Vertex A (–8, 4): \[ A' = (0.25 \times (–8), 0.25 \times 4) = (–2, 1) \]
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Vertex B (–4, 4): \[ B' = (0.25 \times (–4), 0.25 \times 4) = (–1, 1) \]
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Vertex C (0, –8): \[ C' = (0.25 \times 0, 0.25 \times (–8)) = (0, –2) \]
Step 2: Plot the original and dilated triangles
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Original Triangle ABC:
- A(–8, 4)
- B(–4, 4)
- C(0, –8)
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Dilated Triangle A'B'C':
- A'(–2, 1)
- B'(–1, 1)
- C'(0, –2)
Step 3: Graph the triangles
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Original Triangle ABC:
- Plot points A, B, and C on a Cartesian plane.
- Connect the points to form triangle ABC.
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Dilated Triangle A'B'C':
- Plot points A', B', and C' on the same Cartesian plane.
- Connect these points to form the dilated triangle.
Step 4: Visualization
When you graph it, you will see that triangle ABC is larger and located further from the origin compared to its dilated image A'B'C', which will be smaller and closer to the origin.
Multiple Choice Summary
Now, if this is a multiple-choice question, based on the given coordinates, you should be able to find the option that represents triangle ABC with vertices at:
- A(–8, 4)
- B(–4, 4)
- C(0, –8)
And triangle A'B'C' with vertices at:
- A'(-2, 1)
- B'(-1, 1)
- C'(0, -2)
Make sure to choose the answer that most accurately reflects the position and size of both triangles on the graph.