Question

What translation rule can be used to describe the result of the composition of T < 4, −10 >(x, y) and T < −1, −9 >(x, y)?

Answer 1

The first translation picks a point and adds 4 to its x coordinate, and subtracts 10 from the y coordinate. In other words, it moves the point 4 units to the right and 10 units down.

Similarly, the second translation subtracts 1 to the x coordinate, and subtracts 9 from the y coordinate. In other words, it moves the point 1 unit to the left and 9 units down.

So, if you perform one translation after the other, you move the point 4 units to the right and 1 unit to the left along the x axis, and 10 units down and 9 more units down along the y axis.

The net result is a translation of 3 units to the right and 19 units down.