Question

find a single translation that has the same effect as the following composition of translations (x,y)-> (x-5,y+7) followed by (x,y)-> (x+3,y)

Answer 1

Answer:  $(x,y)$ → $(x-2,y+7)$

Step-by-step explanation:

By definition, a Translation is a trasformation in which a figure is moved a fixed distance in a fixed direction. In this type of transformation the size and the shape of the figure does not change.

Composition of transformations happens when two or more transformation are combined. Each transformation is applied on the image of the previous transformation.

In this case we have this Composition of translations:

$(x,y)$ → $(x-5,y+7)$ followed by $(x,y)$ → $(x+3,y)$

You can notice that  5 units are subtracted from the x-coordinate in the first transformation and then 3 units are added. So, the sum is:

$-5+3=-2$

Observe that, in the first transformation, 7 units are added to the y-coordinate and then 0 units are added. The sum is:

$7+0=7$

Then, the single Translation that has the same effect as the given Composition of translation is:

$(x,y)$ → $(x-2,y+7)$