isosceles trapezoid ABCD is shown below with a line ef drawn through its center. Of the isosceles trapezoid is dilated using a scale factor of 1/2 and a line is drawn through the center of the new dilated figure, what relationship will that line have with line EF?
An image shows two dilated figures with lines AB and CD drawn. If the larger figure was dilated using a scale factor of 3, what relationship do lines AB and CD have?
New Line = EF/(1/2) = 2EF.
For the first question, if the isosceles trapezoid ABCD is dilated using a scale factor of 1/2, the line ef drawn through its center will remain the same. The line ef will have the same relationship with the line through the center of the newly dilated figure.
For the second question, if the larger figure was dilated using a scale factor of 3, the relationship between lines AB and CD will also remain the same. The relationship between lines AB and CD will not change with dilation.
To answer the question, we need to understand the properties of a dilated figure.
A dilation is a transformation that changes the size of a figure without changing its shape. When a figure is dilated by a scale factor greater than 1, the resulting figure is larger than the original figure. When a figure is dilated by a scale factor between 0 and 1, the resulting figure is smaller than the original figure.
In the case of the isosceles trapezoid, if it is dilated using a scale factor of 1/2, each side of the original trapezoid will be multiplied by 1/2 to determine the corresponding side of the dilated trapezoid.
Now, since a line is drawn through the center of the dilated figure, this line will pass through the midpoint of the two parallel sides of the trapezoid. Therefore, this line will have the same relationship with line EF as the original line did.
For the second question, if the larger figure was dilated using a scale factor of 3, each side of the original figure will be multiplied by 3 to determine the corresponding side of the dilated figure.
Since lines AB and CD are parallel lines in the original figure, they will remain parallel after dilation. Therefore, the relationship between lines AB and CD will continue to be that of parallel lines in the dilated figure.