Question

△cde is a translation of △cde. write the translation rule.
(x, y) → (x +, y + )

Explanation:

Step1: Find the coordinates of a point and its image

Let's take point \(D\). The coordinates of \(D\) are \((-9,-5)\) and the coordinates of \(D'\) are \((-4,8)\).

Step2: Calculate the change in \(x\) - coordinate

The change in \(x\) - coordinate (\(\Delta x\)) is \(x_{D'}-x_{D}\). So, \(\Delta x=- 4-(-9)=-4 + 9=5\).

Step3: Calculate the change in \(y\) - coordinate

The change in \(y\) - coordinate (\(\Delta y\)) is \(y_{D'}-y_{D}\). So, \(\Delta y=8-(-5)=8 + 5 = 13\).

We can check with another point. Let's take point \(E\). The coordinates of \(E\) are \((-6,-7)\) and the coordinates of \(E'\) are \((-1,6)\).

Step4: Calculate \(x\) - change for \(E\)

\(\Delta x=-1-(-6)=-1 + 6=5\)

Step5: Calculate \(y\) - change for \(E\)

\(\Delta y=6-(-7)=6 + 7=13\)

Answer:

\((x,y)\to(x + 5,y+13)\)