Question

Polygon ABCD is translated to create polygon A′B′C′D′. Point A is located at (1, 5), and point A′ is located at (-2, 3). Which expression defines the transformation of any point (x, y) to (x′, y′) on the polygons

Answer 1

`(x',y')-->(x-3,y-2)`

Explanation:

Notice that we can get from the x-coordinate of A, 1, to the x-coordinte of A', -2, by subtracting 3 from the x-coordinate of A. More formaly:

`1+a=-2`

`a=-2-1`

`a=-3`

Similarly, we can get from the y-coordinate of A, 5, to the y-coordinate of A', 3, by subtracting 2 from the y-coordinte of A. More formaly:

`5+b=3`

`b=3-5`

`b=-2`

Now we now that to get to A' from A, we need to subtract 3 to the x-coordinate of A and subtract 2 to the y-coordinate. Knowing this, we can create the expression to translate any point of the polygon ABCD to create the polygon A'B'C'D':

`(x',y')-->(x-3,y-2)`