Question

1. part a which sequence of transformations maps rectangle abcd onto rectangle abcd? a translation 6 units down, reflection across the x - axis b reflection across the x - axis, translation 6 units right c reflection across the x - axis, translation 6 units left d translation 6 units left, reflection across the y - axis part b describe a sequence of transformations that maps abcd onto abcd. 12. part a which figure is the image of figure a after a reflection across the x - axis and a translation 4 units right? a figure b b figure c c figure d d figure e part b which figure can be transformed into figure g after a rotation 90° about the origin, then a translation 13 units right and 4 units down? a figure b b figure d c figure e d figure f

Explanation:

Step1: Understand reflection across x - axis

When a point $(x,y)$ is reflected across the x - axis, the transformation is $(x,y)\to(x, - y)$.

Step2: Understand translation

A translation of $a$ units right means $(x,y)\to(x + a,y)$ and $a$ units left means $(x,y)\to(x - a,y)$.

Step3: Analyze Part A

For a reflection across the x - axis and a translation 4 units right of Figure A: First, reflect each point of Figure A across the x - axis (change the sign of the y - coordinate). Then move each reflected point 4 units to the right (add 4 to the x - coordinate). By visual inspection of the graphs, we can determine the resulting figure.

Step4: Analyze rotation about origin

A 90 - degree rotation about the origin for a point $(x,y)$ is $(x,y)\to(-y,x)$ for a counter - clockwise rotation.

Step5: Analyze Part B

For a 90 - degree rotation about the origin, then a translation 13 units right and 4 units down of a figure to get Figure G: First, apply the 90 - degree rotation to each point of the original figure. Then apply the translation (add 13 to the x - coordinate and subtract 4 from the y - coordinate). By visual inspection of the graphs, we can determine the starting figure.

Answer:

Part A: Need to visually inspect the graphs after applying the transformation rules to determine the answer.
Part B: Need to visually inspect the graphs after applying the rotation and translation rules to determine the answer.