Unit 7, Lesson 13
Distances in the Coordinate Plane
Accelerated 6
13.1
Warm-up
Plot at least 3 points in your assigned quadrant, and label them with their coordinates.
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Plot at least 3 points in your assigned quadrant, and label them with their coordinates.
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.
and
and
and
Point has the same coordinates as point , except its -coordinate has the opposite sign.
Point has the same coordinates as point , except its -coordinate has the opposite sign.
Point has the same coordinates as point , except both coordinates have opposite signs. In which quadrant is point ?
Plot and label these points in the coordinate plane: , , , .
Connect the dots in order. What shape is made?
What are the side lengths of figure ?
What is the difference between the -coordinates of and ?
What is the difference between the -coordinates of and ?
How do the differences of the coordinates relate to the distances between the points?
Here are the coordinates for four polygons. Plot them on the coordinate plane, connect the points in the order that they are listed, and label each polygon with its letter name.
Polygon A:
Polygon B:
Polygon C:
Polygon D:
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 |