Cartesian Plane — All 4 Quadrants
Sort Points by Quadrant
Sort each ordered pair into the correct quadrant.
Which Quadrant?
Circle the quadrant where each point is located.
(-5, 3)
(4, -2)
(-1, -7)
(6, 1)
More Quadrant Questions
Circle the quadrant.
(8, -4)
(-3, 6)
(2, 9)
(-7, -2)
On an Axis or In a Quadrant?
Circle the correct location.
(0, 5) is:
(-3, 0) is:
(0, 0) is:
(4, 0) is:
Match Sign Pattern to Quadrant
Draw a line to match each sign pattern to its quadrant.
Write the Coordinates
Write an ordered pair in each location.
A point in Quadrant 1: ( ___ , ___ )
A point in Quadrant 2: ( ___ , ___ )
A point in Quadrant 3: ( ___ , ___ )
A point in Quadrant 4: ( ___ , ___ )
A point on the x-axis: ( ___ , ___ )
Match Points to Descriptions
Draw a line to match each point to its description.
Translate the Point
Move as described and write the new coordinates.
Start at (2, 3). Move 5 units left: ( ___ , ___ )
Start at (-1, 4). Move 3 units down: ( ___ , ___ )
Start at (0, -2). Move 4 right and 3 up: ( ___ , ___ )
Start at (-3, -1). Move 6 right and 5 up: ( ___ , ___ )
Reflect the Point
Reflect each point over the specified axis.
Reflect (3, 2) over the x-axis: ( ___ , ___ )
Reflect (3, 2) over the y-axis: ( ___ , ___ )
Reflect (-4, 1) over the x-axis: ( ___ , ___ )
Reflect (-4, 1) over the y-axis: ( ___ , ___ )
Sort Points by Location
Sort each point into the correct location.
Describe the Movement
Describe how to move from the first point to the second.
From (1, 2) to (4, 5): move ___ right and ___ up
From (3, -1) to (-2, -1): move ___ left
From (-3, 4) to (-3, -2): move ___ down
From (0, 0) to (-4, 3): move ___ left and ___ up
Symmetry on the Plane
Circle the correct answer.
If (3, 5) is reflected over the y-axis, the new x-coordinate is:
If (3, 5) is reflected over the x-axis, the new y-coordinate is:
If (-2, 4) is reflected over both axes, the new point is:
Draw a Shape on the Cartesian Plane
Plot these points and connect them. What shape?
Points: (2, 3), (-2, 3), (-2, -3), (2, -3). Shape: ___
Points: (0, 4), (-3, 0), (0, -4), (3, 0). Shape: ___
Find the Missing Vertex
Find the coordinates of the missing corner.
Rectangle corners: (1, 2), (5, 2), (5, -1) and ( ___ , ___ ).
Square corners: (-3, 3), (3, 3), (3, -3) and ( ___ , ___ ).
Coordinate Challenge
Solve these coordinate geometry problems.
What is the midpoint of (-4, 2) to (2, 2)? ___
A point (5, 2) is reflected over both axes. It becomes ( ___ , ___ ).
Distance between (-3, 0) and (5, 0) on the x-axis: ___
Home Activity: Coordinate Treasure Hunt
Use coordinates to explore!
- 1Draw a Cartesian plane. Plot at least 2 points in each quadrant.
- 2Create a treasure map using coordinate clues.
- 3Play battleship using all 4 quadrants.
- 4Draw a picture by connecting plotted points.
- 5Challenge a friend to recreate a coordinate art picture from your instructions.
Distance Between Points on Horizontal and Vertical Lines
Calculate the distance between each pair of points.
A(2, 5) to B(8, 5) — horizontal line. Distance = ___
C(-3, 1) to D(-3, -6) — vertical line. Distance = ___
E(-5, 4) to F(3, 4). Distance = ___
G(0, -7) to H(0, 5). Distance = ___
Midpoint of a Line Segment
Find the midpoint of each line segment.
Midpoint of (-4, 2) and (6, 2): ( ___ , ___ )
Midpoint of (1, -3) and (1, 7): ( ___ , ___ )
Midpoint of (-5, 0) and (3, 0): ( ___ , ___ )
Midpoint of (0, -8) and (0, 4): ( ___ , ___ )
Quadrant After Transformation
In which quadrant is the transformed point?
(3, 5) reflected over y-axis:
(-2, 4) reflected over x-axis:
(1, -3) translated (-3, 5):
(-4, -2) reflected over both axes:
Match Coordinate Patterns
Match each rule to the correct set of points.
Coordinate Geometry Patterns
Describe the coordinate pattern for each.
All points where y = x: list 4 examples: ___
All points where y = -x: list 4 examples: ___
All points where x + y = 0: list 4 examples: ___
Plotting and Connecting Shapes
Plot and connect these points to make each shape. What is its area?
Points: (0,4), (4,0), (0,-4), (-4,0). Shape: ___. Area = ___
Points: (3,3), (-3,3), (-3,-3), (3,-3). Shape: ___. Area = ___
Describing Transformations from Coordinates
Look at the original and new coordinates. Describe the transformation.
Original: (2,3). New: (-2,3). Transformation: ___
Original: (4,-1). New: (4,1). Transformation: ___
Original: (1,2). New: (4,5). Transformation: ___
Original: (-3,5). New: (3,-5). Transformation: ___
Sort Coordinates by Quadrant
Sort each coordinate pair into the correct quadrant.
Graphing Simple Relationships
Plot the points from this table and describe the pattern.
x: 1, 2, 3, 4. y: 2, 4, 6, 8. Describe the rule connecting x and y: ___
x: -2, -1, 0, 1, 2. y: -4, -2, 0, 2, 4. Rule: ___
Geometry on the Cartesian Plane
Use coordinates to solve these geometry problems.
A line goes from (-3, 1) to (5, 1). Length = ___
A square has one vertex at (2, 3) and side length 4. Name all other vertices (multiple answers possible): ___
The perimeter of a triangle with vertices (0,0), (6,0), (0,8): ___
Points Plotted in Each Quadrant
A student plotted 30 points. This graph shows how many in each region. Each icon = 1 point.
| Quadrant 1 | |
| Quadrant 2 | |
| Quadrant 3 | |
| Quadrant 4 |
What fraction of points are in Q1?
Which quadrant has the fewest points?
What percentage of points are in Q3 or Q4?
Sign Patterns of Coordinates
Sort these coordinates by sign pattern.
| Item | Tally | Total |
|---|---|---|
(+,+) — Q1 | ||
(-,+) — Q2 | ||
(-,-) — Q3 | ||
(+,-) — Q4 |
Coordinate Art
Follow the coordinates to complete the drawing.
Connect: (0,5) → (2,2) → (5,2) → (3,0) → (4,-3) → (0,-1) → (-4,-3) → (-3,0) → (-5,2) → (-2,2) → (0,5). What shape does this look like? ___
List 5 of your own points and connect them to make a shape: ___
Real-World Cartesian Plane
Answer these real-world questions about coordinate systems.
Map reading: on a street map, A3 means row A, column 3. How is this like a Cartesian plane? ___
Latitude and longitude: Sydney is about (151°E, 34°S). Describe this as a coordinate pair: ___
Design a simple map using a Cartesian plane with at least 5 labelled places: ___