Solve the Problem $\mathrm { A } ( - 1 , - 2 ) , \mathrm { B } ( 2 , - 3 )$

question 37

Multiple Choice

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 \(\overline { \mathrm { AB } }\) to \(\overline { \mathrm { CD } }\) such that the image of \(\mathrm { A }\) is \(\mathrm { C }\) and the image of \(\mathrm { B }\) is \(D\) is \(( x , y ) \rightarrow ( x + 1 , y + 3 )\).
• B) \(\mathrm { D } ( 3 , - 9 )\); \(A\) translation that takes \(\overline { \mathrm { AB } }\) to \(\overline { \mathrm { CD } }\) such that the image of \(\mathrm { A }\) is \(\mathrm { C }\) and the image of \(\mathrm { B }\) is \(D\) is \(( x , y ) \rightarrow ( x - 3 , y - 1 )\).
• C) \(\mathrm { D } ( 0 , - 9 )\); A translation that takes \(\overline { \mathrm { AB } }\) to \(\overline { \mathrm { CD } }\) such that the image of \(\mathrm { A }\) is \(\mathrm { C }\) and the image of \(\mathrm { B }\) is \(D\) is \(( x , y ) \rightarrow ( x - 2 , y - 6 )\).
• D) \(\mathrm { D } ( - 2 , - 8 )\); A translation that takes \(\overline { \mathrm { AB } }\) to \(\overline { \mathrm { CD } }\) such that the image of \(\mathrm { A }\) is \(\mathrm { C }\) and the image of \(\mathrm { B }\) is \(D\) is \(( x , y ) \rightarrow ( x - 6 , y - 2 )\).

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Definitions:

Share Repurchases

It refers to the process where a company buys back its own shares from the marketplace, reducing the amount of outstanding shares.