Question

1. 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: Analyze reflection across x - axis

When a figure is reflected across the x - axis, the y - coordinates of all its points change sign.

Step2: Analyze translation 4 units right

After reflection, when translating 4 units right, we add 4 to the x - coordinates of all points.

Step3: Check for Part A

By visual inspection of the figure after applying these transformations, we can see that Figure C is the image of Figure A after reflection across the x - axis and translation 4 units right.

Step4: Analyze rotation 90° about origin

For a 90° counter - clockwise rotation about the origin, the transformation rule for a point (x,y) is (-y,x).

Step5: Analyze translation 13 units right and 4 units down

After rotation, we add 13 to the x - coordinate and subtract 4 from the y - coordinate of each point.

Step6: Check for Part B

By visual inspection of the figure after applying these transformations, we can see that Figure D can be transformed into Figure G after the given rotation and translation.

Answer:

Part A: B. Figure C
Part B: B. Figure D