1. 5-5 Distance on the Coordinate Plane!

2. What should I take from this lesson?
Find the distance between two points on the coordinate plane.

3. Step 1: Graph & Label your points.
On a city map, a library is located at (3, 6) and a school is located at (1, 3). Graph the ordered pairs and determine the distance between the library and the school.

4. Step 2: Draw the sides of your triangle.
On a city map, a library is located at (3, 6) and a school is located at (1, 3). Graph the ordered pairs and determine the distance between the library and the school.
(3,6)
(1,3)

5. Step 3: Label the length of the sides of your triangle.
On a city map, a library is located at (3, 6) and a school is located at (1, 3). Graph the ordered pairs and determine the distance between the library and the school.
(3,6)
(1,3)

6. Step 4: Draw the other side of your triangle and set up your equation.
On a city map, a library is located at (3, 6) and a school is located at (1, 3). Graph the ordered pairs and determine the distance between the library and the school.
(3,6) 3 2
a2 + b2 = c2
A=3
B=2
C=?
(1,3)

7. Step 5: Solve for the variable.
On a city map, a library is located at (3, 6) and a school is located at (1, 3). Graph the ordered pairs and determine the distance between the library and the school. Model on geoboard.
(3,6) 3 2
a2 + b2 = c2
= c2
9 + 4 = c2
13 = c2
√13 = c
c = 3.6
(1,3)

8. Step 5: Solve for the variable.
Step 1: Graph & Label your points.
Step 2: Draw the sides of your triangle.
Step 3: Label the length of the sides of your triangle.
Step 4: Draw the other side of your triangle and set up your equation.
Step 5: Solve for the variable.

9. Let’s try it!
Graph the ordered pairs (2, 6) and (5, 2). Then find the distance between the points. Model on geoboard.
(2,6)
(5,2)

10. Let’s try it again!
Graph the ordered pairs (3, 7) and (7, 1). Then find the distance between the points. Model on geoboard.

11. On a city map, a taco shack is located at (6, 4) and Jackie’s house is located at (4, 1). How far away is the taco shack from Jackie’s house? Model on geoboard.
A) 13 units away
B) 3.6 units away
C) -13 units away
D) 5 units away

12. On a city map, a gas station is located at (4, 2) and Josh’s house is located at (9, 6). How far away is the gas station from Josh’s house? Model on geoboard.
A) 5 units away
B) 4 units away
C) 5.8 units away
D) 6.4 units away

13. Step 5: Solve for the variable.
Step 1: Graph & Label your points.
Step 2: Draw the sides of your triangle.
Step 3: Label the length of the sides of your triangle.
Step 4: Draw the other side of your triangle and set up your equation.
Step 5: Solve for the variable.

14. Melissa lives in Chicago, Illinois
Melissa lives in Chicago, Illinois. A unit on the grid of her map shown below is 0.08 mile. Find the distance between McCormickville at (–2, –1) and Lake Shore Park at (2, 2). Model on geoboard.
A) 25 miles away
B) 5 miles away
C) 0.4 miles away
D) 7.16 units away