investigate transformations
1. social studies nautical flags are used by ships for signaling. flipping a flag vertically can be a sign of distress. the flag representing the number 7 is shown. where is the yellow side if the flag is flipped vertically? explain.
2. a quadrilateral has a pair of vertical parallel sides on the left and right of the figure. ryan turns the quadrilateral one - half turn clockwise. where are the parallel lines on the turned figure?
3. does each pair of shapes show a flip, slide, or turn? if so, identify which.
a. two trapezoid - like shapes
b. two quadrilateral shapes
4. attend to precision complete the drawing of the shape slid to the right. two pentagons, one incomplete
5. stem a biologist is studying leaves with line symmetry. complete the biologist’s sketch of the leaf by flipping the shape across the vertical line. a zig - zag triangle shape with vertical dashed line
6. attend to precision complete the drawing of the shape after it has been turned. a square and a partial shape

Question

investigate transformations
1. social studies nautical flags are used by ships for signaling. flipping a flag vertically can be a sign of distress. the flag representing the number 7 is shown. where is the yellow side if the flag is flipped vertically? explain.
2. a quadrilateral has a pair of vertical parallel sides on the left and right of the figure. ryan turns the quadrilateral one - half turn clockwise. where are the parallel lines on the turned figure?
3. does each pair of shapes show a flip, slide, or turn? if so, identify which.
   a. two trapezoid - like shapes
   b. two quadrilateral shapes
4. attend to precision complete the drawing of the shape slid to the right. two pentagons, one incomplete
5. stem a biologist is studying leaves with line symmetry. complete the biologist’s sketch of the leaf by flipping the shape across the vertical line. a zig - zag triangle shape with vertical dashed line
6. attend to precision complete the drawing of the shape after it has been turned. a square and a partial shape

Accepted Answer

### Question 1
# Brief Explanations:
The flag is a triangle - like shape with yellow on top and red at the bottom. A vertical flip (reflection over a vertical line) will reverse the vertical orientation. So the yellow side, which was on the top, will now be on the bottom (or we can think in terms of the position relative to the flag's axis; after flipping vertically, the part that was above the axis is now below and vice - versa).
# Answer:
After flipping the flag vertically, the yellow side will be at the bottom (or the lower part of the flag). The vertical flip is a reflection, and it swaps the top and bottom (in terms of the vertical position of the yellow region) of the flag.

### Question 2
# Brief Explanations:
A one - half turn (180 - degree rotation) of a quadrilateral with vertical parallel sides (left and right) will make the left and right sides become horizontal. Because a 180 - degree rotation changes the orientation of the sides. If the original sides were vertical (parallel to the y - axis), after a 180 - degree rotation, they will be parallel to the x - axis (horizontal), and they will be the top and bottom sides of the rotated quadrilateral.
# Answer:
After a one - half turn clockwise, the pair of parallel lines (which were vertical on the left and right) will be horizontal (on the top and bottom) of the turned figure.

### Question 3
#### Part A
# Brief Explanations:
The two shapes are mirror images of each other across a vertical (or some) line. A flip (reflection) is a transformation that produces a mirror image. So this pair of shapes shows a flip.
# Answer:
A. Flip

#### Part B
# Brief Explanations:
The second shape looks like it has been rotated (turned) relative to the first shape. The orientation of the shape has changed in a way that is consistent with a rotation (turn) rather than a slide (translation) or a flip (reflection).
# Answer:
B. Turn

### Question 4
# Brief Explanations:
To complete the drawing of the shape slid (translated) to the right, we need to move each vertex of the original pentagon to the right by the same distance as the given partial drawing. The original pentagon has vertices, and we replicate the shape by shifting each point horizontally to the right so that the new shape is congruent and in the correct position (aligned with the partial drawing provided).
# Answer:
(The drawing should be a congruent pentagon to the original, shifted to the right such that it aligns with the partial pentagon shown. Each vertex of the original pentagon is moved horizontally to the right by the appropriate distance to form the complete slid shape.)

### Question 5
# Brief Explanations:
To complete the leaf by flipping (reflecting) across the vertical line, we take each point of the given part of the leaf and find its mirror image across the vertical line. For a point $(x,y)$ relative to the vertical line $x = a$, the reflected point will be $(2a - x,y)$. We use this reflection rule to draw the other half of the leaf so that it is symmetric across the vertical line.
# Answer:
(The drawing should be the mirror image of the given part of the leaf across the vertical dashed line. Each vertex of the given part is reflected across the vertical line to form the complete leaf with line symmetry.)

### Question 6
# Brief Explanations:
To complete the drawing after the shape has been turned (rotated), we first determine the angle of rotation. From the given shapes, we can see that we need to rotate the original shape (the rectangle - like shape) to match the orientation of the partial drawing. We rotate each vertex of the original shape by the appropriate angle (probably 90 degrees or 180 degrees, depending on the context) and then draw the rotated shape to complete it.
# Answer:
(The drawing should be the rotated version of the original rectangle - like shape. Each vertex is rotated by the correct angle (e.g., if it's a 90 - degree turn, the sides will change from horizontal/vertical to vertical/horizontal in the appropriate way) to form the complete turned shape.)

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