Final Answer:
The resulting image of the isosceles triangle FGH under a dilation with a scale factor of 0.5 will be a reduction. The triangle will be smaller in size compared to the preimage due to the scale factor being less than 1, causing a reduction in dimensions.
Explanation:
In a dilation, the scale factor determines whether the resulting image will be an enlargement or a reduction. A scale factor greater than 1 enlarges the preimage, while a scale factor less than 1 reduces its size. Here, a scale factor of 0.5 implies that the resulting image will be half the size of the preimage in all dimensions. In the case of isosceles triangle FGH, applying a dilation with a scale factor of 0.5 will proportionally shrink the triangle, making it smaller in size compared to the original.
To visualize this, if the sides of the isosceles triangle FGH were, for example, 10 units each, applying a dilation with a scale factor of 0.5 would reduce the sides to half their length, resulting in sides of 5 units each in the image. Consequently, all corresponding lengths and dimensions of the triangle will be reduced by a factor of 0.5, leading to a smaller and proportionally scaled-down image compared to the preimage.
Therefore, under the given dilation with a scale factor of 0.5, the resulting image of isosceles triangle FGH will exhibit a reduction in size, making it smaller in proportion to the original triangle due to the scale factor being less than 1.