Question

your turn

1. use coordinate notation to write the rule that maps each preimage to its

image. then identify the transformation. graph the image ( r ^ { prime } s ^ { prime } t ^ { prime } ) to check
your answer.
preimage
( r ( - 4,3 ) )
( s ( - 1,3 ) )
( t ( - 4,1 ) )
image
( r ^ { prime } ( 1 , - 1 ) )
( s ^ { prime } ( 4 , - 1 ) )
( t ^ { prime } ( 1 , - 3 ) )
the coordinate rule is:
the transformation is:

Explanation:

Step1: Find the change in \(x\)-coordinate

For point \(R(-4,3)\) and its image \(R'(1,-1)\), the change in \(x\)-coordinate is \(1-(-4)=5\).
For point \(S(-1,3)\) and its image \(S'(4,-1)\), the change in \(x\)-coordinate is \(4 - (-1)=5\).
For point \(T(-4,1)\) and its image \(T'(1,-3)\), the change in \(x\)-coordinate is \(1-(-4)=5\).

Step2: Find the change in \(y\)-coordinate

For point \(R(-4,3)\) and its image \(R'(1,-1)\), the change in \(y\)-coordinate is \(-1 - 3=-4\).
For point \(S(-1,3)\) and its image \(S'(4,-1)\), the change in \(y\)-coordinate is \(-1 - 3=-4\).
For point \(T(-4,1)\) and its image \(T'(1,-3)\), the change in \(y\)-coordinate is \(-3 - 1=-4\).

Step3: Write the coordinate rule

The coordinate rule for a translation is \((x,y)\to(x + 5,y-4)\)

Answer:

The coordinate rule is \((x,y)\to(x + 5,y - 4)\) and the transformation is a translation \(5\) units to the right and \(4\) units down.