Question

writing a rule for a translation
which rule describes the translation?
○ (x, y) → (x - 8, y - 3)
○ (x, y) → (x - 3, y + 8)
○ (x, y) → (x + 8, y - 3)
○ (x, y) → (x + 3, y + 8)

Explanation:

Step1: Determine the horizontal translation

Let's assume a point \( B\) with \( x\) - coordinate \( x_1=-6\) and its image \( B'\) has \( x\) - coordinate \( x_2 = 2\). The change in \( x\) is \( \Delta x=x_2 - x_1=2-(-6)=8\). A positive change in \( x\) means a shift to the right. So the rule for the \( x\) - coordinate is \( x\to x + 8\).

Step2: Determine the vertical translation

Let's assume a point \( B\) with \( y\) - coordinate \( y_1 = 2\) and its image \( B'\) has \( y\) - coordinate \( y_2=-1\). The change in \( y\) is \( \Delta y=y_2 - y_1=-1 - 2=-3\). A negative change in \( y\) means a shift downwards. So the rule for the \( y\) - coordinate is \( y\to y-3\).

Answer:

\((x,y)\to(x + 8,y - 3)\) (the third option)