Question

quadrilateral abcd is a translation of quadrilateral abcd. what is the rule for the translation? (x, y) → (x + 2, y + 5) (x, y) → (x - 2, y - 5)

Explanation:

Step1: Observe x - coordinate change

Take a point, say A(4, 2). Its image A'(2, - 3). The change in x - coordinate is \(2-4=-2\).

Step2: Observe y - coordinate change

For point A(4, 2) and A'(2, - 3), the change in y - coordinate is \(-3 - 2=-5\).

Step3: Determine the translation rule

For any point \((x,y)\) in the original figure, the rule for translation to the new point \((x',y')\) is \(x'=x - 2\) and \(y'=y - 5\), so the rule is \((x,y)\to(x - 2,y - 5)\).

Answer:

\((x,y)\to(x - 2,y - 5)\)