Question

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)

Answer 1

don't have an answer but have a good day :)

Answer 2

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.

Answer 3

Thank you! Have a great day too!