Unit 7, Lesson 14
Distances in the Coordinate Plane
Grade 6
14.1
Warm-up
Plot at least 3 points in your assigned quadrant, and label them with their coordinates.
14.2
Activity
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Write the coordinates of each point.
Coordinate plane, origin O, horizontal axis negative 7 through 7 by ones, vertical axis negative 5 through 5 by ones. Point A is 4 units to the right of the origin and 3 units up. Point B is 6 units down from point A. Point C is 1 unit to the left and 2 units down from point B. Point D is 7 units to the left and 2 units up from point C. Point E is 2 units to the left and 6 units up from point D. -
Answer these questions for each pair of points.
- How are the coordinates the same? How are they different?
- How far away are they from the -axis? To the left or to the right of it?
- How far away are they from the -axis? Above or below it?
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and
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and
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and
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Point has the same coordinates as point , except its -coordinate has the opposite sign.
- Plot point in the coordinate plane, and label it with its coordinates.
- How far away are and from the -axis?
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Point has the same coordinates as point , except its -coordinate has the opposite sign.
- Plot point in the coordinate plane, and label it with its coordinates.
- How far away are and from the -axis?
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Point has the same coordinates as point , except both coordinates have opposite signs. In which quadrant is point ?
14.3
Activity
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Label each point with its coordinates.
Coordinate plane, origin O, hoizontal axis negative 7 through 7 by ones, vertical axis negative 5 through 5 by ones. Point A is 1 point 5 units to the left and 2 units up from the origin. Point B is 5 units to the right of point A. Point C is 5 units to the right and 5 units down from point A. Point D is 5 units to the right and 6 point 5 units down from point A. Point E is 6 point 5 units directly below point A. -
Find the distance between each pair of points.
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Points and
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Points and
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Points and
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Which of the points are 5 units from ?
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Which of the points are 2 units from ?
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Plot a point that is both 2.5 units from and 9 units from . Label that point , and write down its coordinates.
Student Lesson Summary
The points , and are shown in the coordinate plane. Notice that they all have almost the same coordinates, except the signs are different. They are all the same distance from each axis but are in different quadrants.
Notice that the vertical distance between points and is 4 units because point is 2 units above the horizontal axis and point is 2 units below the horizontal axis. The horizontal distance between points and is 10 units because point is 5 units to the left of the vertical axis and point is 5 units to the right of the vertical axis.
We can always tell which quadrant a point is located in by the signs of its coordinates.
| quadrant | ||
|---|---|---|
| positive | positive | I |
| negative | positive | II |
| negative | negative | III |
| positive | negative | IV |
None