Line AB and line CD are parallel lines. Line AB contains the points A(−5,−5) and B(−3,−2), and line CD contains the points C(−7,−2,) and D(−5,1). Describe the effect of the dilation with a scale factor of 3 and a center point of dilation at the origin (0,0).
Option #1: After dilation, the lines are three units farther from the point of dilation. The resulting points are A′ (−2,−2), B′ (0,1), C′(−4,1), and D′(−2,4). The dilated lines are parallel.
Option #2: After dilation, the lines are three units closer to the point of dilation. The resulting points are A′ (−53,−53), B′(−1,−23), C′(−72,−23), and D′(−53,13). The dilated lines are parallel.
Option #3: After dilation, the lines are three units farther from the point of dilation. The resulting points are A′(−15,−15), B′(−9,−6), C′(−21,−6), and D′(−15,3). The dilated lines are parallel.
(1 point)
The correct answer is Option #3: After dilation, the lines are three units farther from the point of dilation. The resulting points are A′(−15,−15), B′(−9,−6), C′(−21,−6), and D′(−15,3). The dilated lines are parallel.
This is because a dilation with a scale factor of 3 multiplies the coordinates of each point by 3, resulting in the points being three times as far from the origin. In this case, the original points are multiplied by 3 to give the new points: A′(−15,−15), B′(−9,−6), C′(−21,−6), and D′(−15,3).
Since the original lines AB and CD are parallel, and a dilation preserves parallelism, the dilated lines A'B' and C'D' will also be parallel.
don't have an answer but have a good day :)
Thank you! Have a great day too!
The correct option is Option #3: After dilation, the lines are three units farther from the point of dilation. The resulting points are A′(−15,−15), B′(−9,−6), C′(−21,−6), and D′(−15,3). The dilated lines are parallel.
To describe the effect of a dilation with a scale factor of 3 and a center point of dilation at the origin, we need to understand what a dilation is.
A dilation is a transformation that changes the size of an object. In this case, the object we are dilating is the set of points on each line. A scale factor of 3 means that each point on the line will be multiplied by 3 in both the x-coordinate and the y-coordinate.
Let's calculate the coordinates of the new points after the dilation:
For point A(-5,-5), the new x-coordinate would be -5 * 3 = -15, and the new y-coordinate would be -5 * 3 = -15. So, the new coordinates for A would be A'(-15,-15).
For point B(-3,-2), the new x-coordinate would be -3 * 3 = -9, and the new y-coordinate would be -2 * 3 = -6. So, the new coordinates for B would be B'(-9,-6).
For point C(-7,-2), the new x-coordinate would be -7 * 3 = -21, and the new y-coordinate would be -2 * 3 = -6. So, the new coordinates for C would be C'(-21,-6).
For point D(-5,1), the new x-coordinate would be -5 * 3 = -15, and the new y-coordinate would be 1 * 3 = 3. So, the new coordinates for D would be D'(-15,3).
Now we can examine the options:
Option #1: After dilation, the lines are three units farther from the point of dilation. The resulting points are A′(−2,−2), B′(0,1), C′(−4,1), and D′(−2,4). The dilated lines are parallel.
Option #2: After dilation, the lines are three units closer to the point of dilation. The resulting points are A′ (−53,−53), B′(−1,−23), C′(−72,−23), and D′(−53,13). The dilated lines are parallel.
Option #3: After dilation, the lines are three units farther from the point of dilation. The resulting points are A′(−15,−15), B′(−9,−6), C′(−21,−6), and D′(−15,3). The dilated lines are parallel.
Based on our calculations, we can see that Option #3 is the correct one. After dilation, the lines are three units farther from the point of dilation, and the resulting points are A′(−15,−15), B′(−9,−6), C′(−21,−6), and D′(−15,3). The dilated lines are parallel.