Use the image to answer the question.
"The x-axis of a coordinate plane ranges from negative 7 to 12 and the y-axis ranges from negative 7 to 6, both in 1-unit increments. Three points are plotted, one of which serves as the origin for two rays. The points are labeled upper D, upper E, and upper F. Upper D is located at left parenthesis negative 2 comma negative 4 right parenthesis. Upper E is located at left parenthesis 2 comma 1 right parenthesis. Upper F is located at left parenthesis 3 comma negative 3 right parenthesis.
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).
(1 point)
Use the image to answer the question.
"The x-axis of a coordinate plane ranges from negative 7 to 12 and the y-axis ranges from negative 7 to 6, both in 1-unit increments. Three points are plotted, one of which serves as the origin for two rays. The points are labeled upper D, upper E, and upper F. Upper D is located at left parenthesis negative 2 comma negative 4 right parenthesis. Upper E is located at left parenthesis 2 comma 1 right parenthesis. Upper F is located at left parenthesis 3 comma negative 3 right parenthesis.
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).
(1 point)
The correct answer is 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).
The correct option is 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).
To determine 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), we need to understand how dilation works.
Dilation is a transformation that changes the size of an object without changing its shape. In this case, a scale factor of 4 means that all distances in the dilated figure will be four times larger than in the original figure. The center of dilation is the point about which the figure is enlarged or reduced.
Let's apply the scale factor of 4 to the given points D(-2, -4), E(2, 1), and F(3, -3):
Dilation of point D:
x-coordinate: -2 * 4 = -8
y-coordinate: -4 * 4 = -16
Dilated point D': (-8, -16)
Dilation of point E:
x-coordinate: 2 * 4 = 8
y-coordinate: 1 * 4 = 4
Dilated point E': (8, 4)
Dilation of point F:
x-coordinate: 3 * 4 = 12
y-coordinate: -3 * 4 = -12
Dilated point F': (12, -12)
Based on these calculations, we can conclude that Option #1 is the correct answer:
"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)."