Using the coordinate plane will help us find the perimeter and area of different shapes. You first draw the shape on the coordinate plane and then you can count the number of unit squares the shape takes up. For perimeter, it's the number of unit squares that go around the shape.

**Example 1 : **

The grid shows the path Tommy followed when he walked from his home at (0, 0) to various locations and back home again. If each grid square represents one block, how many blocks did he walk ?

**Solution : **

**Step 1 :**

Find each distance. Each grid unit represents one block.

Tommy’s home (0, 0) to the library (0, 4) is

|4| − 0 = 4 − 0 = 4 blocks.

The library (0, 4) to the park (5, 4) is

|5| − 0 = 5 − 0 = 5 blocks.

The park (5, 4) to Tommy’s friend’s house (5, 2) is

|4| − |2| = 4 − 2 = 2 blocks.

Tommy’s friend’s house (5, 2) to the pond (7, 2) is

|7| − |5| = 7 – 5 = 2 blocks.

The pond (7, 2) to the store (7, 0) is

|2| − 0 = 2 − 0 = 2 blocks.

The store (7, 0) to Tommy’s home (0, 0) is

|7| − 0 = 7 − 0 = 7 blocks

**Step 2 :**

Find the sum of the distances.

Tommy walked 4 + 5 + 2 + 2 + 2 + 7 = 22 blocks.

**Example 2 : **

Suppose the next day Tommy walks from his home to the mall at (0, 8), and then walks to a movie theater at (7, 8). After leaving the theater Tommy walks to the store at (7, 0) before returning home. How far does he walk ?

**Solution : **

The above situation has been illustrated in the graph given below.

**Step 1 :**

Find each distance. Each grid unit represents one block.

Tommy’s home (0, 0) to the mall (0, 8) is

|8| − 0 = 8 − 0 = 8 blocks.

The mall (0, 8) to the theater (7, 8) is

|7| − 0 = 7 − 0 = 7 blocks.

The theater (7, 8) to the store (7, 0) is

|8| − 0 = 8 − 0 = 8 blocks.

The store (7, 0) to Tommy’s home (0, 0) is

|7| − 0 = 7 − 0 = 7 blocks

**Step 2 :**

Find the sum of the distances.

Tommy walked 8 + 7 + 8 + 7 = 30 blocks.

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