Final answer:
After applying a dilation factor of 1/2 to Sarah's picture, the new dimensions become 3 inches long and 4 inches wide.
Step-by-step explanation:
Sarah wants to reduce the size of her picture by a dilation factor of 1/2. To find the new dimensions of her picture, we multiply the original dimensions by the dilation factor. The original dimensions are 6 inches in length and 8 inches in width.
The new length is calculated as follows:
Original Length × Dilation Factor = 6 inches × 1/2 = 3 inches long.
The new width is calculated as:
Original Width × Dilation Factor = 8 inches × 1/2 = 4 inches wide.
Therefore, Sarah's picture will now measure 3 inches in length and 4 inches in width after the reduction.