Question

Adair performed a transformation on a triangle with pre-image coordinates

D(3, 0), E(2, 3), and F(4, 3). The coordinates of the image are D'(6, 0), E'(4, 6),
and F'(8, 6). She challenges her friend Stacy to describe the transformation.
Which response is correct?
A.The pre-image was dilated by a scale factor of
B.The pre-image was dilated by a scale factor of 2.
C.The pre-image was translated 3 units to the right.
D. The pre-image was translated 3 units to the left.

Answer 1

The correct description of the transformation on the triangle with pre-image coordinates D(3, 0), E(2, 3), and F(4, 3) that led to image coordinates D'(6, 0), E'(4, 6), and F'(8, 6) is a dilation by a scale factor of 2.

Step-by-step explanation:

Adair performed a transformation on a triangle with the pre-image coordinates D(3, 0), E(2, 3), and F(4, 3). The transformed image coordinates are D'(6, 0), E'(4, 6), and F'(8, 6). To determine the type of transformation that occurred, we can compare the coordinates of the pre-image and image. We can see that the x-coordinates of the image points are twice that of the pre-image points, and the y-coordinates of the image points are also twice that of the pre-image points.

For example, point D is at (3, 0) and D' is at (6, 0). The x-coordinate has been multiplied by 2. Similarly, for points E and F, both the x- and y-coordinates have been multiplied by the same factor of 2. This indicates that the transformation is a dilation with a scale factor of 2. Hence, the correct response to Adair's challenge to describe the transformation is B. The pre-image was dilated by a scale factor of 2.