Question

describing single in the coordinate plane continued. 6 quadrilateral pqrs is transformed in the coordinate plane to form the image pqrs. label the vertices of pqrs and tell what single transformation was used. 7 triangle fgh is transformed in the coordinate plane to form the image fgh. label the vertices of fgh and tell what single transformation was used. 8 draw a figure and an image of that figure in such a way that any of the three transformations (a single translation, a single reflection, or a single rotation) could be used to obtain it.

Explanation:

Step1: Analyze transformation of quadrilateral PQRS

By observing the position of PQRS and P'Q'R'S' on the coordinate - plane, we can see that each point (x,y) of PQRS is transformed to (x,y - 6). This is a vertical translation.

Step2: Analyze transformation of triangle FGH

By observing the position of FGH and F'G'H' on the coordinate - plane, we can see that FGH is rotated 180° about the origin. If a point (x,y) in FGH is rotated 180° about the origin, it becomes (-x,-y).

Step3: Draw a figure and its image for part 8

For example, draw a square with vertices (1,1), (1,3), (3,3), (3,1). A translation of 2 units to the right would give vertices (3,1), (3,3), (5,3), (5,1). A reflection across the x - axis would give vertices (1, - 1), (1, - 3), (3, - 3), (3, - 1). A 90° rotation about the origin would give vertices (-1,1), (-3,1), (-3,3), (-1,3).

Answer:

1. P'Q'R'S' is obtained by a vertical translation of 6 units down.
2. F'G'H' is obtained by a 180° rotation about the origin.
3. See the above - described examples for drawing a figure and its image for different single transformations.