Question

The vertices of ▲ XYZ are X (6,-5), Y (3,0), Z (-4, 9). A XYZ is translated 3 units left and 8 units up. Then, it is translated 2 units right and 6 units down. What is the final translation rule that maps the pre-image to the final image?

Answer 1

After the first translation, the coordinates of the vertices of the triangle will be X (3,-13), Y (0,-8), Z (-7, 1). After the second translation, the coordinates of the vertices will be X (5,-7), Y (2,-2), Z (-5, 7).

The final translation rule that maps the pre-image to the final image is a translation of 2 units right and 6 units up. This can be written as a translation rule of the form (x, y) -> (x + 2, y + 6).

Explanation:

Answer 2

After the first translation the coordinates are:

• (x, y) → (x - 3, y + 8)

After the second translation the coordinates are:

• (x - 3, y + 8) → (x - 3 + 2, y + 8 - 6) = (x - 1, y + 2)

The final translation rule is:

• (x, y ) → (x - 1, y + 2)

or

• One unit left and 2 units up.