Question

Quadrilateral ABCD is dilated by a scale factor of 1 over 3 centered around (1, 2).

quadrilateral ABCD shown on coordinate plane with coordinates at 1 comma 2, 2 comma 3, 4 comma 2, and 2 comma 1

Which statement is true about the dilation?

Answer 1

It should be C: segment B prime D prime will be parallel to segment BD and will be shorter than segment BD.

Explanation:

Answer 2

Dilating quadrilateral ABCD by a scale factor of 1/3 centered around the point (1, 2) involves scaling and repositioning its vertices. The new coordinates are calculated using the dilation center and the scale factor. In a related example, a proportion is used to find the actual dimension when a scale dimension and scale factor are known.

To solve the problem of finding the dilated coordinates of quadrilateral ABCD by a scale factor of 1/3 centered around the point (1, 2), we apply the dilation process which alters the dimensions of the figure. The new coordinates can be found by subtracting the center of dilation from the original coordinates, multiplying by the scale factor, and then adding the center of dilation back to the scaled coordinates. This way, if the original coordinate is (x, y), the dilated coordinate will be ((x-1)*1/3+1, (y-2)*1/3+2).

Here's an example using the scale measurement proportion principle in a different context. If the scale dimension is 4 inches and the actual dimension needs to be found with a given scale factor of 1:2, the proportion is 1:2=4:x, with x being the actual dimension we want to find. Solving this proportion x = 4 * 2/1, which gives x = 8 inches.