Final answer:
To write coordinates after dilation with a scale factor of 4, multiply the original coordinates by 4. For instance, if the original vertex is (2, 3), the new coordinates will be (8, 12). The same multiplication rule applies to determine any vertices after dilation.
Step-by-step explanation:
In a dilation centered at the origin, the coordinates of a point will change based on the scale factor. To write the coordinates of the vertices after a dilation with a scale factor of 4 centered at the origin, you multiply the x and y coordinates of each vertex by the scale factor. For example, if you have a vertex at coordinates (x, y), after the dilation, the new coordinates will be (4x, 4y).
Example 1: If the original coordinates are (2, 3), after the dilation with a scale factor of 4, the new coordinates will be (8, 12).
Similarly, you can apply this rule for any vertex of the figure to find the coordinates after dilation.
To find the missing actual dimension if the scale factor is 1/4":4' and the scale measurement is 8", you would set up the proportion in the following way:
1/4"/4' = 8"/x
Solve for x to find the actual dimension.