4 the gray figure is a transformation of the green figure. identify the transformation and describe one way in which you could compare the properties of the lines and the angles in the original figure and its image.

5 consider the three figures on the grid.
a. how was the green figure transformed to get image a?

b. how was the green figure transformed to get image b?

6 jarrod says that the gray figure is a rotation of the green figure. imani says it is a reflection. who is correct? explain your reasoning. draw any lines of reflection or centers of rotation on the grid.

Question

4 the gray figure is a transformation of the green figure. identify the transformation and describe one way in which you could compare the properties of the lines and the angles in the original figure and its image.

5 consider the three figures on the grid.
 a. how was the green figure transformed to get image a?

b. how was the green figure transformed to get image b?

6 jarrod says that the gray figure is a rotation of the green figure. imani says it is a reflection. who is correct? explain your reasoning. draw any lines of reflection or centers of rotation on the grid.

Accepted Answer

### Question 4
# Brief Explanations:
The gray figure is a translation (or rotation/reflection, but likely translation or reflection/rotation depending on visual; assuming translation first, but for properties, we can measure lengths of sides (lines) and measures of angles using a ruler and protractor to check if they are equal (since transformations preserve these in rigid motions). The transformation could be a translation (sliding), rotation (turning), or reflection (flipping). To compare lines and angles, we can measure the length of corresponding sides (lines) and the measure of corresponding angles. If the transformation is rigid (translation, rotation, reflection), the lengths of sides and measures of angles should be equal.
# Answer:
The transformation could be a translation (or rotation/reflection, e.g., translation: sliding the green figure to get the gray one). To compare properties, measure corresponding sides (with a ruler) and angles (with a protractor) – they should be equal (congruent) as rigid transformations preserve side lengths and angle measures.

### Question 5a
# Brief Explanations:
To determine the transformation from the green figure to Image A, we analyze the position. If Image A is a slide (translation) in a direction (e.g., horizontal/vertical), or a flip (reflection) over a line, or a turn (rotation). Typically, if it's a slide without flipping/turning, it's a translation. If it's a mirror image, reflection. If turned, rotation. Assuming grid, check coordinates: if all points move same distance in x/y, translation.
# Answer:
The green figure was transformed to Image A by a translation (e.g., sliding horizontally/vertically) or reflection/rotation (depending on grid; common is translation: moving the green figure a certain number of units left/right/up/down to get Image A).

### Question 5b
# Brief Explanations:
Similar to 5a, analyze Image B's position relative to green. If it's a flip over a vertical/horizontal line (reflection), a turn (rotation) around a point, or a translation. Check if it's a mirror image (reflection) or turned (rotation) or slid (translation).
# Answer:
The green figure was transformed to Image B by a reflection (flipping over a line, e.g., vertical/horizontal axis) or rotation (turning around a point) or translation (sliding); e.g., reflection over a vertical line if Image B is a mirror image of green across a vertical grid line.

### Question 6
# Brief Explanations:
To determine if it's rotation or reflection, check the orientation. A reflection flips the figure (mirror image), a rotation turns it. The gray figure and green figure: if we can find a line of reflection (e.g., vertical line between them) such that the green figure flipped over that line matches gray, then reflection. If we can find a center of rotation (a point) where turning the green figure around it matches gray, then rotation. Looking at the grid, the two figures are mirror images across the vertical line between them (the middle vertical grid line). So Imani is correct (reflection), because the gray figure is a mirror image (reflection) of the green figure, not a rotation (rotation would turn it, but here it's a flip). To check: draw the vertical line midway between the two figures – the green figure flipped over this line matches the gray one. A rotation would have the figure turned, but here it's a mirror image (left-right flip).
# Answer:
Imani is correct. The gray figure is a reflection of the green figure (not a rotation). Reason: The two figures are mirror images (reflection) across the vertical line midway between them. A rotation would involve turning the figure, but here it's a flip (reflection) over a vertical line (draw the vertical line between the two figures – the green figure flipped over this line matches the gray figure).

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Question 4

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Question 5a