Exercise 26 Page 179

The horse moved 1 unit down and 2 units to the right. When writing the translation this is equivalent to subtract 1 from the y-value and add 2 to the x-value. Translation:(x,y) → (x+2,y-1)

Translation for the Second Move

We will do the same thing as we did for the first move. By identifying how many units we will have to shift to get from the red horse to the final destination, we can form the second translation.

First the horse moved 1 unit to the right and then 2 units down. Therefore, we will have to add 1 to the x-coordinate and remove 2 from the y-coordinate to get to the ending position. Translation: (x,y) → (x+1,y-2)

Combining the Translations

Now that we have written both translations, we can write them as one. We need to calculate the total number of units moved horizontally and the total number of units moved vertically. Let's start with horizontal, the x-coordinate, by comparing the two translations. First Translation: &x → x+2 Second Translation: &x → x+1 Total Translation: &x → x+3 Therefore, the horse moved a total of 3 units to the right. Now we will do the same thing for the y-value. First Translation: &y → y-1 Second Translation: &y → y-2 Total Translation: &y → y-3 From the original position to the ending position the horse moved 3 units down. With the total translation for the x- and y-value we can now write a single translation. Single Translation: (x,y) → (x+3,y-3) To make sure we written the correct translation, we will test it on the horse to see if it takes us from the original position to the ending position. First we will move 3 units to the right and then 3 units down.

As we can see in the picture, the translation took us to the endpoint and is correct!