To dilate a figure from the origin with a given magnitude, you multiply the coordinates of each vertex by that magnitude.
Let's say the original coordinates of the triangle's vertices are:
- A(x₁, y₁)
- B(x₂, y₂)
- C(x₃, y₃)
For a dilation by a magnitude of 3, the new coordinates (A', B', C') will be:
- A' = (3 * x₁, 3 * y₁)
- B' = (3 * x₂, 3 * y₂)
- C' = (3 * x₃, 3 * y₃)
Since we don't have the original coordinates given in your question, let’s evaluate the provided options based on the knowledge of how dilation works.
We know:
- Dilation by a factor of 3 means that each coordinate of the points will be multiplied by 3.
- If the original vertices were, for example, A(−2, −5), then A' would be (3 * −2, 3 * −5) = (−6, −15).
Now let’s check each of the provided options:
- A′(−6,−15), B′(0,9), and C′(18,−9) - This indicates the vertices could represent a dilation of A(−2, −5), and B(0, 3), and C(6, −3).
- A′(−23,−53), B′(0,1), and C′(2,−1) - This does not appear to represent a dilation by a factor of 3 correctly.
- A′(1,−2), B′(3,6), and C′(9,0) - This also does not appear to represent a dilation by a factor of 3 correctly.
- A′(−5,−8), B′(−3,0), and C′(3,0) - This similarly does not seem to represent a correct dilation.
Based on this analysis, the correct response that matches a multiplication by 3 of reasonable original coordinates is:
A′(−6,−15), B′(0,9), and C′(18,−9).
3 answers