To find the new coordinates of the vertices of the parallelogram after dilating it from the origin with a magnitude of 3, we need to multiply each coordinate of the original vertices by 3.
Let’s say the original coordinates of the vertices of the parallelogram are \( E(x_1, y_1) \), \( F(x_2, y_2) \), \( G(x_3, y_3) \), \( H(x_4, y_4) \).
The coordinates of the new vertices after dilation would be calculated as follows:
- For \( E' \): \( E'(3x_1, 3y_1) \)
- For \( F' \): \( F'(3x_2, 3y_2) \)
- For \( G' \): \( G'(3x_3, 3y_3) \)
- For \( H' \): \( H'(3x_4, 3y_4) \)
Since the specific original coordinates of the vertices are not provided in your question, we cannot calculate the new coordinates directly.
However, if we consider the options given:
- E′(2,8), F′(5,11), G′(7,7) and H′(4,4)
- E′(−4,2), F′(−1,5), G′(1,1) and H′(−2,−2)
- E′(−3,15), F′(6,24), G′(12,12) and H′(3,3)
We can see that:
- The first option has coordinates that are not scaled appropriately.
- The second option also presents coordinates that do not reasonably suggest a dilation by 3.
- The third option suggests values that look like they might result from proper scaling.
Thus, without the specific original coordinates, it’s reasonable to consider E′(−3,15), F′(6,24), G′(12,12) and H′(3,3) as the probable correct response, given that they seem furthest from zero by a factor consistent with dilation by 3.
If you have specific coordinates for the original vertices, please provide them, and I can confirm the correct transformed coordinates based on those.
3 answers