Question

polygon abcd is translated to create polygon ( abcd ). point a is located at ( (1,5) ), and point ( a ) is located at ( (-2,3) ). which expression defines the transformation of any point ( (x,y) ) to ( (x,y) ) on the polygons?
( x = x - 3 )
( y = y - 2 )
( x = x - 2 )
( y = y - 3 )
( x = x - 1 )
( y = y - 8 )
( x = x + 3 )
( y = y + 2 )

Explanation:

Step1: Calculate the change in x - coordinate

For the x - coordinate, we have \(x = 1\) (original x - coordinate of point A) and \(x'=-2\) (new x - coordinate of point A).
The change in x is \(x' - x=-2 - 1=-3\), so \(x'=x+( - 3)=x - 3\).

Step2: Calculate the change in y - coordinate

For the y - coordinate, we have \(y = 5\) (original y - coordinate of point A) and \(y' = 3\) (new y - coordinate of point A).
The change in y is \(y' - y=3 - 5=-2\), so \(y'=y+( - 2)=y - 2\).

Answer:

\(x'=x - 3\), \(y'=y - 2\) (the first option)