Lesson 7.8Ordered Pairs in All Four Quadrants
Start hereWords, worked example, and sentence starters
Learning target I can plot ordered pairs in all four quadrants of the coordinate plane.
Why This Matters Captain Vega realized her treasure map only covered one corner of the island! She needs to expand the map in all directions — north, south, east, and west of the base camp at the origin (0, 0). Now clues can have negative coordinates: (-4, 3) means 4 units west and 3 units north. A clue at (2, -5) means 2 units east and 5 units south. Which quadrant is each clue in?
Start hereWords for this lesson
Read each word before you begin. Say it out loud.
| Word | What it means | Example |
|---|---|---|
| QuadrantSpanish: Cuadrante | One of the four parts of a coordinate grid, numbered I to IV. | I (+, +) top-right, II (-, +) top-left, III (-, -) bottom-left, IV (+, -) bottom-right |
| Negative coordinateSpanish: Coordenada negativa | A coordinate less than zero. It means left or below the center point. | (-3, 2) means 3 left and 2 up from the origin |
| ReflectionSpanish: Reflexión | A flipped, mirror image across a line. | (3, 2) reflected over the y-axis is (-3, 2) — same distance, opposite side |
| AxisSpanish: Eje | One of the two number lines that frame a graph: the x-axis runs across, the y-axis runs up and down. | The x-axis goes left-right; the y-axis goes up-down; they cross at (0, 0) |
| IntegerSpanish: Número entero | Whole numbers and their opposites, like -2, -1, 0, 1, 2. | ..., -3, -2, -1, 0, 1, 2, 3, ... |
How it worksWorked example
These numbers are not on your problems. The steps are. Follow them with your own numbers.
I will plot (-3, -4). I start at the origin (0, 0).
- The x is -3, which is negative, so I move 3 units to the LEFT.
- The y is -4, which is negative, so I move 4 units DOWN. I place my dot.
- Both coordinates are negative, so the point is in Quadrant III.
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
Now let's plot (-5, 2). The x is -5, so which way do we move? Left 5 units.
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- In Quadrant , the x-coordinate is and the y-coordinate is . I know (-3, -4) is in Quadrant because both coordinates are .
Word bank QuadrantNegative coordinateReflectionAxisIntegerquadrantpositivenegativex-coordinatey-coordinateleftright
Watch out!A common mistake
A common mistake in Ordered Pairs in All Four Quadrants is matching each sign to the wrong axis
Lesson 7.8Ordered Pairs in All Four Quadrants
Level 0Most support · every hint printed
Learning target I can plot ordered pairs in all four quadrants of the coordinate plane.
Why This Matters Captain Vega realized her treasure map only covered one corner of the island! She needs to expand the map in all directions — north, south, east, and west of the base camp at the origin (0, 0). Now clues can have negative coordinates: (-4, 3) means 4 units west and 3 units north. A clue at (2, -5) means 2 units east and 5 units south. Which quadrant is each clue in?
How it worksWorked example
These numbers are not on your problems. The steps are. Follow them with your own numbers.
I will plot (-3, -4). I start at the origin (0, 0).
- The x is -3, which is negative, so I move 3 units to the LEFT.
- The y is -4, which is negative, so I move 4 units DOWN. I place my dot.
- Both coordinates are negative, so the point is in Quadrant III.
-
1Write the letter of the matching item on each line.
Match each ordered pair to its quadrant.
- (3, 4)
- (-2, 5)
- (-6, -1)
- (1, -3)
- (-4, 2)
- (5, -6)
- AQuadrant I
- BQuadrant II
- CQuadrant III
- DQuadrant IV
- EQuadrant II
- FQuadrant IV
Steps to try- Only the SIGNS matter: (+, +), (-, +), (-, -), and (+, -) each belong to one quadrant.
- Use the sign map: I = (+, +), II = (-, +), III = (-, -), IV = (+, -). Read each pair's signs and look them up.
- Start with (3, 4): both positive, so Quadrant I. Now read the signs of (-2, 5) and use the map.
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2Circle the letter of the best answer. Show how you know.
In which quadrant is the point (-4, 5)?
- AQuadrant I
- BQuadrant III
- CQuadrant II
- DQuadrant IV
Steps to try- Look at the signs: x = -4 is negative and y = 5 is positive.
- Negative x means move LEFT; positive y means move UP. Ask which corner of the plane is left-and-up.
- From the origin, slide left 4 and climb up 5. Quadrants count I, II, III, IV counterclockwise from top-right.
Show your work -
3Circle the letter of the best answer. Show how you know.
A point has a positive x-coordinate and a negative y-coordinate. Which quadrant is it in?
- AQuadrant I
- BQuadrant II
- CQuadrant IV
- DQuadrant III
Steps to try- Positive x pushes you RIGHT; negative y drops you DOWN.
- Find the corner that is right of the y-axis and below the x-axis. Quadrants I–IV go counterclockwise from top-right.
- Try a sample point like (3, -2): go right 3, then down 2. See which corner of the grid that lands in.
Show your work -
4Circle the letter of the best answer. Show how you know.
Which point is located on the x-axis?
- A(-4, -4)
- B(0, 4)
- C(4, 0)
- D(4, 4)
Steps to try- A point ON the x-axis never moves up or down — its height is zero.
- Check each pair's y-coordinate (the second number). On the x-axis, the y must be 0.
- Read the second number in each pair. A point sits on the x-axis only when that number is 0.
Show your work
Explain your thinkingHow do the signs of the x- and y-coordinates tell you which quadrant a point is in?
Sentence starter In Quadrant ___, the x-coordinate is ___ and the y-coordinate is ___. I know (-3, -4) is in Quadrant ___ because both coordinates are ___.