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Algebra
Question

Triangle \( A ^ { \prime } B ^ { \prime } C ^ { \p...

Triangle \( A ^ { \prime } B ^ { \prime } C ^ { \prime } \) is the image of triangle \( A B C \) under a dilation centered about the origin. Triangle \( A B C \) has vertices \( A ( 10,12 ) , B ( 12,9 ) , \) and \( C ( 10,7 ) . \) Triangle \( A ^ { \prime } B ^ { \prime } C ^ { \prime } \) has vertices \( A ^ { \prime } ( \frac { 15 } { 2 } , 9 ) , B ^ { \prime } ( 9 , \frac { 27 } { 4 } ) , \) and \( C ^ { \prime } ( \frac { 15 } { 2 } , \frac { 21 } { 4 } ) . \) Which rule represents the dilation? 

A) \( D ( x , y ) = ( \frac { 3 } { 4 } x , \frac { 3 } { 4 } y ) \) 

B) \( D ( x , y ) = ( \frac { 3 } { 4 } x , \frac { 3 } { 4 } - y ) \) 

C) \( D ( x , y ) = ( \frac { 3 } { 4 } - x , \frac { 3 } { 4 } - y ) \) 

D) \( D ( x , y ) = ( \frac { 1 } { 4 } x , \frac { 1 } { 4 } y )\) 

Answer

Option A

Solution
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