Learning Goal: Plot rational numbers and ordered pairs, and use signs to find opposites and quadrants.
Vocabulary
coordinate planeA grid made by a horizontal x-axis and vertical y-axis crossing at the origin.
ordered pairTwo numbers (x, y) that name a point's location.
originThe point (0, 0) where the two axes cross.
quadrantOne of four regions of the plane, numbered I to IV counterclockwise.
What You Need to Know
The opposite of a number flips its sign; the opposite of −6 is 6.
In an ordered pair (x, y), x moves left/right and y moves up/down.
Quadrant I is (+, +), II is (−, +), III is (−, −), and IV is (+, −).
Flipping the sign of one coordinate reflects the point across an axis.
Flipping the signs of both coordinates reflects the point across both axes.
Points on an axis (like (0, 4) or (−3, 0)) are not inside any quadrant.
Worked Example I Do — watch how it works
In which quadrant is the point (−4, 3)? Then give its reflection across the y-axis.
Step 1. The x-value is negative and the y-value is positive: (−, +).
Step 2. (−, +) is Quadrant II.
Step 3. Reflecting across the y-axis flips the x-sign: (−4, 3) becomes (4, 3).
Answer: Quadrant II; reflection is (4, 3)
Guided Practice We Do — try it together
1. What is the opposite of 3.5?
💡 Hint: Keep the distance from zero, flip the sign.
2. In which quadrant is (5, −2)?
💡 Hint: Positive x with negative y is (+, −).
3. Reflect (2, 6) across the x-axis.
💡 Hint: Reflecting across the x-axis flips the y-sign.
Independent Practice You Do — show your work
1. What is the opposite of the opposite of −7?
2. In which quadrant is the point (−1, −8)?
3. Reflect the point (−3, 4) across the y-axis.
4. Name the quadrant of (6, 7).
5. Is the point (0, −5) in a quadrant? Explain in a few words.
MCAP-Style Practice
Directions: Answer each item the way you would on the MCAP. For selected-response items, fill in the circle (○) next to the correct answer. For constructed-response items, enter your answer and show your work. Every item below assesses standard 6.NS.C.6.
Item 1Selected Response6.NS.C.6
Point A is at (−4, 3). Point B is its reflection across the x-axis. What are the coordinates of B?
Select the correct answer.
Item 2Selected Response6.NS.C.6
A point has a negative x-coordinate and a positive y-coordinate. Which quadrant is it in?
Select the correct answer.
Item 3Constructed Response6.NS.C.6
Are (3, −5) and (3, 5) reflections across the x-axis? Explain in a few words.
Enter your answer in the space provided. Show your work.
Enter your answer:
Teacher Answer Key (click to show)
Independent 1
−7
Independent 2
Quadrant III
Independent 3
(3, 4)
Independent 4
Quadrant I
Independent 5
No; it is on the y-axis.
Item 1 · 6.NS.C.6
B — Reflecting across the x-axis keeps x and flips the y-sign: (−4, 3) to (−4, −3).
Item 2 · 6.NS.C.6
B — (−, +) is the upper-left region, which is Quadrant II.
Item 3 · 6.NS.C.6
Yes — same x, opposite y. — Reflecting across the x-axis keeps the x-coordinate and flips the sign of the y-coordinate.
Neft Teacher · Grade 6 MCAP Mathematics Review · Standard 6.NS.C.6