Final answer:
Dilations in geometry are performed by multiplying each coordinate of the vertices of a figure by a scale factor to obtain the vertices of the dilated figure, whether it is a triangle or any other shape. Examples provided include calculating the scaled length of a flower bed and finding missing dimensions using given proportions.
Step-by-step explanation:
To dilate each triangle with point P as the center of dilation and a given scale factor, one must understand that dilation is a transformation that alters the size of a figure proportionally in geometry. The scale factor determines how much larger or smaller the image will be compared to the original figure.
For example, in the case of Leah wanting to make a scale drawing of a flower bed with the longest side being 5.5 meters and a scale factor of 1/20, the length of the longest side on her drawing would be:
5.5 meters * 1/20 = 0.275 meters.
In the case of a scale factor provided as 2 inches to 3 feet with a scale measurement of 6 inches, one can write the proportion to find the missing actual dimension by setting up the proportion 2 inches/3 feet = 6 inches/x feet, and solve for x.
When dilating with respect to a variable scale factor such as a, the coordinates of each vertex of the original triangle are multiplied by a to determine the coordinates of the vertices of the dilated triangle.