Activities

1. You are out with your family running errands on a Saturday afternoon.  You start out at your house located at (3,5).  The first person you have to drop off is your brother at the park for his baseball game.  You drive 8 blocks west to the park. From the park you now have to go to school because you forgot to bring home your math homework.  From the park, you drive 6 blocks south. Lastly you have to stop at the grocery store to pick up a few items.  From the school, you drive 12 blocks east.  What are the coordinates of the park, school and grocery store? 

Park    ______________ 

School            ______________

Grocery Store ______________

2. Construct rectangle ABCD on the coordinate plane that has one vertex in each quadrant; and all sides are vertical or horizontal lines.  Plot and label each point on the provided grid.

3. Draw a horizontal line segment starting at (2. -3) that has a length of 6 units and the other endpoint in the third quadrant.  What are the coordinates of the other endpoint of the line segment?

4. Consider the points (-2, 0) and (7, 0).

a. What do the ordered pairs have in common and what does that mean about their location on the coordinate plane?
b. Find the distance between the two numbers on the coordinate grid using absolute value.  Explain how to use this method.

5. Consider the line segment with endpoints (-4, 3) and (7, 0)

a. What do the endpoints, which are represented by the ordered pairs, have in common?  What does that tell us about the look and location of the line segment on the coordinate plane?
b. Find the length of the line segment by finding the distance between its endpoints using absolute value.  Explain what you did.

6. Judy and Anthony were working on the same problem in math class.  They each started at the point (-2. 5) and moved 4 units vertically on a coordinate plane.  Each of them arrived at a different endpoint.  How is this possible?  Explain and list the two different endpoints.

Answer Key/Rubric

1. Park (-5, 5)
   
   School (-5, -1)
   
   Grocery Store (7, -1)
   
   
2. Answers will vary but must include a point in each quadrant that will satisfy all the requirements needed when they are connected to make a rectangle. Students must label each point.

3. Coordinates are (-4,-3)
   

4. 
   a. Both of their y-coordinates are zero so each point lies on the x-axis, the horizontal number line.
   b. Calculate the absolute values of the numbers, which tells us how far the numbers are from zero.  If the numbers are located on opposite sides of zero, then add their absolute values together.  If the numbers are located on the same side of zero, then subtract their absolute values.= 2 and = 7. The numbers are on opposite sides of zero, so the absolute values get combined:  2 + 7 = 9.  The distance between (-2, 0)  and (7, 0) is 9 units.

5. 
   a. Both endpoints have x-coordinates of -4, so the points lie on the vertical line that intersects the x-axis at -4.  This means that the endpoints of the line segment lie on a vertical line.
   b.  = 3 and   = 5.  The numbers are on opposite sides of zero, so the absolute values get added:  3 + 5 = 8.  The distance between(-4, 3) and (-4 -5) is 8 units.
   
   
6. It is possible to have two different ending points.
   
   Reasons might include, but are not limited to:

• One student could have counted up and the other could have counted down.
• Moving 4 units in either direction vertically would generate the following possible endpoints:  (-2, 9) or (-2, 1).