Question

The image of the point (0,9) under a translation is (1,7). Find the coordinates ofthe image of the point (-9,3) under the same translation.

Answer 1

The coordinates of image of the point (-9,3) is;

`(-8,1)`

Step-by-step explanation:

Given that;

The image of the point (0,9) under a translation is (1,7).

Let us find the rule of the translation;

`(0,9)\rightarrow(1,7)`

Let us find the change in each axis;

`\begin{gathered} \Delta x=1-0=1 \\ \Delta y=7-9=-2 \end{gathered}`

So, the rule of the translation will be;

`\begin{gathered} (x,y)\rightarrow(x+\Delta x,y+\Delta y) \\ (x,y)\rightarrow(x+1,y-2) \end{gathered}`

Now that we have the rule, let us apply it to get the image of the point (-9,3);

`\begin{gathered} (x,y)\rightarrow(x+1,y-2) \\ (-9,3)\rightarrow(-9+1,3-2) \\ (-9,3)\rightarrow(-8,1) \end{gathered}`

Therefore, the coordinates of image of the point (-9,3) is;

`(-8,1)`