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Unit 8 - Lesson 11 - Grade 8: Illustrative Mathematics

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Grade 8 Unit 8
Lesson 11: Finding Distances in the Coordinate Plane
CC BY 2021 Illustrative Mathematics®
Grade 8 Unit 8
Lesson 11: Finding Distances in the Coordinate Plane
CC BY 2021 Illustrative Mathematics®
Lesson: Finding Distances in the Coordinate Plane

Closest Distance (Warm Up)

1.

Order the following pairs of coordinates from closest to farthest apart.

(2, 4) and (2,10)
(-3, 6) and (5, 6)
(-12, -12) and (-12, -1)
(7, 0) and (7,-9)
(1, -10) and (-4, -10)

  1. (7, 0) and (7,-9)
  2. (-3, 6) and (5, 6)
  3. (1, -10) and (-4, -10)
  4. (-12, -12) and (-12, -1)
  5. (2, 4) and (2,10)
2.

Explain your reasoning.

3.

Name another pair of coordinates that would be closer together than the first pair on your list.

4.

Name another pair of coordinates that would be farther apart than the last pair on your list.

How Far Apart?

5.

Find the distances between the three points shown.


Perimeters with Pythagoras (Optional)

6.

Which figure do you think has the longer perimeter?

7.

Select one figure and calculate its perimeter. Your partner will calculate the perimeter of the other. Were you correct about which figure had the longer perimeter?

Finding the Right Distance

Have each person in your group select one of the sets of coordinate pairs shown here. Then calculate the length of the line segment between those two coordinates. Once the values are calculated, have each person in the group briefly share how they did their calculations.
  • (-3, 1) and (5, 7)
  • (-1, -6) and (5, 2)
  • (-1, 2) and (5, -6)
  • (-2, -5) and (6, 1)
8.

How does the value you found compare to the rest of your group?


9.

In your own words, write an explanation to another student for how to find the distance between any two coordinate pairs.


Cool Down: Lengths of Line Segments

Lengths of Line Segments

10.

Here are two line segments with lengths e and f. Calculate the exact values of e and f. Which is larger?