Question

The image of point (-2,3) under translation T' is (3,-1). What is the image of point (4,2) under thesame translation?

Answer 1

A translation will add an amount to each coordinate, this amount can be different by each coordinate, but it will be the same for any points that undergo the sam translation.

So, if the translation got the point from (-2, 3) to (3, -1), we see that:

`\begin{gathered} x\colon-2\to3 \\ T_x=3-(-2)=3+2=5 \\ \\ y\colon3\to-1 \\ T_y=-1-3=-4_{} \end{gathered}`

So, the translation was 5 units to the right and 4 units down. Now, we can apply the same to the point (4, 2):

`\begin{gathered} x\colon4+5=9 \\ y\colon2-4=-2 \end{gathered}`

So, the image is (9, -2).