Solve the problem.
-Points

\mathrm { A } ( - 1 , - 2 ) , \mathrm { B } ( 2 , - 3 )

, and

\mathrm { C } ( - 3 , - 8 )

are given. Find all possible coordinates of point

\mathrm { D }

such that the four points form a rectangle. For each location of point D found, find a translation that will take

\overline { \mathrm { AB } }

to the opposite side of the rectangle formed.

A)

\mathrm { D } ( 1 , - 11 )

; A translation that takes

\overline { \mathrm { AB } }

\overline { \mathrm { CD } }

such that the image of

\mathrm { A }

\mathrm { C }

and the image of

\mathrm { B }

D

( x , y ) \rightarrow ( x + 1 , y + 3 )

.
B)

\mathrm { D } ( 3 , - 9 )

;

A

translation that takes

\overline { \mathrm { AB } }

\overline { \mathrm { CD } }

such that the image of

\mathrm { A }

\mathrm { C }

and the image of

\mathrm { B }

D

( x , y ) \rightarrow ( x - 3 , y - 1 )

.
C)

\mathrm { D } ( 0 , - 9 )

; A translation that takes

\overline { \mathrm { AB } }

\overline { \mathrm { CD } }

such that the image of

\mathrm { A }

\mathrm { C }

and the image of

\mathrm { B }

D

( x , y ) \rightarrow ( x - 2 , y - 6 )

.
D)

\mathrm { D } ( - 2 , - 8 )

; A translation that takes

\overline { \mathrm { AB } }

\overline { \mathrm { CD } }

such that the image of

\mathrm { A }

\mathrm { C }

and the image of

\mathrm { B }

D

( x , y ) \rightarrow ( x - 6 , y - 2 )

Solve the Problem. -Find the Image of the Given Figure Under the Reflection

Multiple Choice