Question

question: 11
which describes a possible sequence of transformations that transforms polygon g h j k into polygon ghjk?
a 180 - degree rotation about the origin,
a followed by a dilation centered at the origin with a scale factor of \\( \frac { 1 } { 2 } \\)
a reflection across the line \\( y = x \\), followed by
b a dilation centered at the origin with a scale factor of 2
a reflection across the y - axis, followed by a
c reflection across the x - axis, followed by a dilation centered at the origin with a scale factor of 2
a reflection across the y - axis, followed by a
d translation down 10 units, followed by a dilation centered at the origin with a scale factor of \\( \frac { 1 } { 2 } \\)
question: 12
two figures are shown on the coordinate plan.
describe a series of transformations to show the relationship between figure 1 and figure 2. include all the necessary information to complete the transformation, which includes a description of the transformations and the relationship between the two figures.

Explanation:

Step1: Analyze the size change

The smaller polygon \(G'H'J'K'\) is half the size of \(GHJK\). A dilation with a scale factor of \(\frac{1}{2}\) is involved.

Step2: Analyze the position change

Reflect \(GHJK\) across the \(y -\)axis. Then translate it down 10 units. This series of transformations (reflection across \(y -\)axis, translation down 10 units, dilation with scale factor \(\frac{1}{2}\)) matches option D.

Answer:

D. a reflection across the y - axis, followed by a translation down 10 units, followed by a dilation centered at the origin with a scale factor of \(\frac{1}{2}\)