Question

find the transformation Matrix that the square ABCD whose center is as (2,2) reduced the half of its size with center still remaining at(2,2) the coordinates of squre ABCD at A(0,0) B(0,4) C(4,4) D(4,0) find the coordinates of new squre​

Answer 1

Given :   square ABCD whose center is as (2,2) reduced the half of its size with center still remaining at(2,2) the coordinates of squre ABCD at A(0,0) B(0,4) C(4,4) D(4,0)

To Find : transformation Matrix

the coordinates of new square​

Solution:

A ( 0 , 0)  

B  ( 0 , 4)

C (  4 , 4)

D ( 4, 0)

Center of square ( 2, 2)

transformation Matrix that find the square ABCD whose center is as (2,2) reduced the half of its size with

Transformation would be

(x + 2)/2 , ( y + 2)/2

As Center is ( 2, 2) instead of zero and size is half

A' = ( 0 + 2)/2  , ( 0 + 2)/2  = (  1, 1)

B' = ( 0 + 2)/2 , (4 + 2)/2  =   (  1 , 3)

C' = ( 4 + 2)/2  , ( 4 + 2)/2  = (  3, 3)

D' = ( 4 + 2)/2 , (0 + 2)/2  =  (  3 , 1 )

T(x , y) = (x + 2)/2 , ( y + 2)/2 is the transformation .

Coordinates of new square

A' =  (  1, 1)

B' =  (  1 , 3)

C' =   (  3, 3)

D' =  (  3 , 1 )

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