The image of point g after a dilation with center (0, 0) and a scale factor of 1 can be understood through the concept of dilations in geometry.
A dilation is a transformation that alters the size of a figure while maintaining its shape. The center of dilation is the fixed point around which the transformation occurs. In this case, our center is (0, 0).
When we apply a dilation with a scale factor of 1, it means that each point in the figure, in this instance point g, retains its original distance from the center. In practical terms, the transformation will take each point and multiply its coordinates by the scale factor. Here’s the mathematical representation:
Image of g = (x, y) ↦ (scale factor × x, scale factor × y)
Image of g = (x, y) ↦ (1 × x, 1 × y) = (x, y)Thus, the image of point g after the dilation with a scale factor of 1 will remain exactly the same as the original point g. There is no change in its position.
In summary, when a dilation with a scale factor of 1 is performed, the image of any point, including point g, is identical to its original coordinates. Thus, the answer is:
- Image of g = g
To visualize this, you can imagine marking point g on a coordinate plane. After performing the dilation, the point would still be located at the same spot, demonstrating that a scale factor of 1 does not change the size or position of a point.