Erin started with one corner of a figure located at $(−4,5)$ and translated it to end at $(6,8)$. To find out how far the shape moved horizontally, she decided to find the difference between the two $x$-coordinates. She wrote: $6−(−4)$.

1. When Erin simplified $6−(−4)$ she got $2$ as her answer. Is this correct? If not, what is the correct simplification?

   Hint (a):

   Did Erin subtract correctly?

2. Write another expression to find out how far the shape moved vertically (↕). Simplify both expressions and describe the translation.

   Hint (b):

   To determine the vertical movement, find the difference between the vertical components of each point by subtracting the upper point from the lower point.

   Answer (b):

   Vertical translation: $8−5=3$

   The shape moved $10$ units right and $3$ units up.

3. Describe each of the translations below.

   1. $(3,−2)→(5,−9)$  

   2. $(−1,4)→(6,−2)$ 

   3. $(0,0)→(-4,−7)$  

   4. $(−2,−9)→(2,9)$