Describe the effect of the dilation of the angle DEF
with a scale factor of 4 and a center point of dilation at the origin (0,0)
. Enter the option number of your response.
Option #1: After dilation, the lines are four times farther from the point of dilation. The angle measurement remains the same. Corresponding lines (rays) are parallel between the angle and the dilated angle. The resulting points are D′(−8,−16)
, E′(8,4)
, and F′(12,−12)
.
Option #2: After dilation, the lines are four times farther from the point of dilation. The angle measurement remains the same. Corresponding lines (rays) are parallel between the angle and the dilated angle. The resulting points are D′(2,0)
, E′(6,5)
, and F′(7,1)
.
Option #3: After dilation, the lines are four times closer to the point of dilation. The angle measurement remains the same. Corresponding lines (rays) are parallel between the angle and the dilated angle. The resulting points are D′(−12,−1)
, E′(12,14)
, and F′(34,−34)
Option #1: After dilation, the lines are four times farther from the point of dilation. The angle measurement remains the same. Corresponding lines (rays) are parallel between the angle and the dilated angle. The resulting points are D′(−8,−16), E′(8,4), and F′(12,−12).
How
When an angle is dilated with a scale factor of 4 and a center of dilation at the origin (0,0), each point of the angle is multiplied by the scale factor to determine the new location after dilation.
For example, the point D (-2, -4) in the original angle DEF is multiplied by a scale factor of 4 to get D' (-8, -16) in the dilated angle.
Similarly, the point E (2, 1) is multiplied by 4 to get E' (8, 4), and the point F (3, -3) is multiplied by 4 to get F' (12, -12).
The resulting points D', E', and F' form the dilated angle, which maintains the same angle measurement but is four times farther from the origin due to the scale factor of 4. The corresponding lines (rays) are parallel between the original angle and the dilated angle.