Quadrants and Reflections

Lesson 2 of 2: The Full Coordinate Plane

In this lesson:

• Discover the four quadrants by plotting, not memorizing
• Reflect points across the axes using sign changes
• Plot rational coordinates anywhere in the plane

What You Will Be Able to Do

1. Identify the quadrant of an ordered pair from its coordinate signs
2. Reflect a point across an axis or the origin using sign changes
3. Plot rational ordered pairs anywhere in the coordinate plane
4. Recognize when a point is on an axis — not in any quadrant

You Already Know Quadrant I

In Grade 5, you plotted points like in the first quadrant.

• : move 3 units right from the origin
• : move 2 units up
• The point lands in the upper-right region

What happens when the coordinates go negative?

Signs Tell You Which Direction to Move

-coordinate → horizontal direction

• Positive : right of the -axis
• Negative : left of the -axis

-coordinate → vertical direction

• Positive : above the -axis
• Negative : below the -axis

Plot One Point Per Region

The Four Quadrants — Derived from the Picture

Summary of the picture — not a rule to memorize.

Name the Quadrant from Signs

Example 1:

• : left of the -axis
• : above the -axis
• Upper-left region → Quadrant II

Example 2:

• : right of the -axis
• : below the -axis
• Lower-right region → Quadrant IV

Quick Check: Reason From Signs

Which quadrant does belong to?

Is right or left? Is up or down?

Commit to your answer before the next slide.

Reflections: The Axis as a Fold Line

Which Sign Flips in Each Reflection?

Reflect across the -axis — keep , flip sign of

Reflect across the -axis — keep , flip sign of

Reflect across the origin — flip both signs

Worked Examples: Reflecting

Starting point: in Quadrant IV

• Reflect across the -axis → flip sign of :
• Reflect across the -axis → flip sign of :
• Reflect across the origin → flip both signs:

Predict Before Seeing the Answer

The reflection of across the -axis is:

• A. — flip the sign of
• B. — swap the two coordinates

Pick A or B before moving on. There's a reason this one trips people up.

Swap vs. Reflection — Three Different Points

Reflection changes a sign. A swap changes which coordinate is which — that's a different point entirely.

Extend to Any Rational Ordered Pair

Any rational pair works the same way as the integers we just plotted.

• Move units left or right (sign of gives direction)
• Move units up or down (sign of gives direction)
• Lesson 1 number-line skill — now applied in two directions

Points on the Axes Have No Quadrant

• — Quadrant IV (right, below)
• — Quadrant III (left, below)
• — on the -axis — not in any quadrant
• — on the -axis — not in any quadrant

Quick Check: Axes Are Borders

Which quadrant does belong to?

It has a negative — but where does it actually sit?

A Treasure Map Uses a Coordinate Grid

• Cabin — the origin
• Well — Quadrant II
• Oak tree — Quadrant IV
• Buried chest — Quadrant III

Which Treasure-Map Pair Are Reflections?

• Well and Chest : same ; -magnitudes differ (4 vs. 5) — not exact reflections
• Oak and Well : different and different — not reflections
• A true reflection needs: same coordinate, opposite signs, equal magnitudes

What to Remember From This Lesson

✓ Coordinate signs give the quadrant — derive from the picture

✓ Reflect across -axis: flip ; -axis: flip ; origin: flip both

Reflection flips a sign: , not

Coordinate = 0 → point is on an axis, no quadrant

Coming Up: Ordering and Absolute Value

You can now place any rational number pair in the plane.

In the next lesson, you will use position to compare — absolute value measures how far a point sits from 0, and that gives you a way to order any list of signed numbers.