Question

use the coordinate - plane to complete parts (a) through (d).
(a) plot the given points and connect them with straight lines in the order given. connect the last point to the first point to complete the figure. label the figure a. (-3, - 6), (-3, - 3), (0, 0), (3, - 3), (3, - 6), (0, - 3)
(b) translate the figure in part (a) - 3 units vertically. label the image b.
(c) translate the figure in part (a) 6 units vertically and 3 units horizontally. label the image c.
(d) translate the figure in part (a) - 3 units horizontally and 6 units vertically. label the image d.
stretch
suppose you repeatedly translate a point at the origin c units horizontally and d units vertically.
(1) write the coordinates of the translated point when you repeat the translation n times.

Explanation:

Step1: Plot points for figure A

Plot the points (-3,-6), (-3,-3), (0,0), (3,-3), (3,-6), (0,-3) on the coordinate - plane and connect them in order and then connect the last to the first to form figure A.

Step2: Translate figure A vertically for figure B

To translate a point (x,y) - 3 units vertically, we use the rule (x,y)→(x,y - 3).
For (-3,-6): (-3,-6-3)=(-3,-9)
For (-3,-3): (-3,-3 - 3)=(-3,-6)
For (0,0): (0,0 - 3)=(0,-3)
For (3,-3): (3,-3 - 3)=(3,-6)
For (3,-6): (3,-6 - 3)=(3,-9)
For (0,-3): (0,-3 - 3)=(0,-6)
Plot these new points and label the figure B.

Step3: Translate figure A for figure C

To translate a point (x,y) 6 units vertically and 3 units horizontally, we use the rule (x,y)→(x + 3,y+6).
For (-3,-6): (-3 + 3,-6 + 6)=(0,0)
For (-3,-3): (-3 + 3,-3 + 6)=(0,3)
For (0,0): (0 + 3,0 + 6)=(3,6)
For (3,-3): (3 + 3,-3 + 6)=(6,3)
For (3,-6): (3 + 3,-6 + 6)=(6,0)
For (0,-3): (0 + 3,-3 + 6)=(3,3)
Plot these new points and label the figure C.

Step4: Translate figure A for figure D

To translate a point (x,y) - 3 units horizontally and 6 units vertically, we use the rule (x,y)→(x - 3,y+6).
For (-3,-6): (-3-3,-6 + 6)=(-6,0)
For (-3,-3): (-3-3,-3 + 6)=(-6,3)
For (0,0): (0-3,0 + 6)=(-3,6)
For (3,-3): (3-3,-3 + 6)=(0,3)
For (3,-6): (3-3,-6 + 6)=(0,0)
For (0,-3): (0-3,-3 + 6)=(-3,3)
Plot these new points and label the figure D.

Step5: Find coordinates for repeated translation

If we start with the point (0,0) and translate it c units horizontally and d units vertically n times, the coordinates of the translated point are (nc,nd).

Answer:

For part (a): Figure A is plotted with given points.
For part (b): Figure B has points (-3,-9), (-3,-6), (0,-3), (3,-6), (3,-9), (0,-6).
For part (c): Figure C has points (0,0), (0,3), (3,6), (6,3), (6,0), (3,3).
For part (d): Figure D has points (-6,0), (-6,3), (-3,6), (0,3), (0,0), (-3,3).
For part (e): The coordinates of the translated point are (nc,nd).