Question

unit 1 retest: rigid transformations and co
look at the graph.
which best explains the transformation?
a translation following the rule (x,y)→(x + 4,y + 9)
a translation following the rule (x,y)→(x - 4,y - 9)
a translation following the rule (x,y)→(x + 9,y + 4)
a translation following the rule (x,y)→(x - 9,y - 4)

Explanation:

Step1: Analyze x - coordinate change

Pick a point, say A(1,6). Its image A' is at (- 3, - 3). The change in the x - coordinate is \(\Delta x=-3 - 1=-4\).

Step2: Analyze y - coordinate change

The change in the y - coordinate for point A is \(\Delta y=-3 - 6=-9\).

Step3: Determine the translation rule

For a translation \((x,y)\to(x + a,y + b)\), here \(a=-4\) and \(b = - 9\), so the rule is \((x,y)\to(x - 4,y - 9)\).

Answer:

A translation following the rule \((x,y)\to(x - 4,y - 9)\)