Question

which rule represents the translation below? (x,y)→(x - 3,y + 5) (x,y)→(x - 5,y + 3) (x,y)→(x + 5,y - 3) (x,y)→(x + 3,y - 5)

Explanation:

Step1: Observe the translation

To find the translation rule, we look at the change in the \(x\) - coordinate and \(y\) - coordinate of a point. Let's take a point on the original triangle, say \(D\). If we assume the coordinates of \(D\) are \((x,y)\) and the coordinates of its corresponding point \(D'\) on the translated triangle.

Step2: Analyze \(x\) - coordinate change

By counting the grid - squares, we see that the \(x\) - coordinate of each point of the original figure increases by 5. For example, if a point has \(x\) - coordinate \(x\) in the original figure, its \(x\) - coordinate in the translated figure is \(x + 5\).

Step3: Analyze \(y\) - coordinate change

The \(y\) - coordinate of each point of the original figure decreases by 3. That is, if a point has \(y\) - coordinate \(y\) in the original figure, its \(y\) - coordinate in the translated figure is \(y-3\). So the translation rule is \((x,y)\to(x + 5,y - 3)\).

Answer:

\((x,y)\to(x + 5,y - 3)\)