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Signs in the
Coordinate Plane

Learn how positive and negative signs in ordered pairs tell you exactly which quadrant a point lives in, and how reflections flip points across the axes.

6th Grade Math

What Is the Coordinate Plane?

The coordinate plane is formed by two number lines that cross at a point called the origin \((0, 0)\). The horizontal line is the \(x\)-axis and the vertical line is the \(y\)-axis. Together they divide the plane into four quadrants.

x y (0, 0) Q I Q II Q III Q IV (+, +) (−, +) (−, −) (+, −)

Ordered Pairs and Their Signs

Every point is written as an ordered pair \((x, y)\). The sign of each number tells you a direction:

\(x\) value
Positive \(\rightarrow\) right of origin
Negative \(\rightarrow\) left of origin
\(y\) value
Positive \(\rightarrow\) above origin
Negative \(\rightarrow\) below origin

Signs Determine the Quadrant

The combination of positive and negative signs in \((x, y)\) places the point in exactly one quadrant:

Quadrant I
\((+, +)\): both positive
Quadrant II
\((-, +)\): \(x\) negative, \(y\) positive
Quadrant III
\((-, -)\): both negative
Quadrant IV
\((+, -)\): \(x\) positive, \(y\) negative

The Sign Rule for Quadrants

x y A (3, 4) B (−3, 4) C (−3, −4) D (3, −4)

Reflection Across the \(y\)-Axis

When two ordered pairs differ only by the sign of \(x\), the points are mirror images across the \(y\)-axis. The \(y\)-value stays the same.

P (4, 3) P' (−4, 3) same y change sign of x

Reflection Across the \(x\)-Axis

When two ordered pairs differ only by the sign of \(y\), the points are mirror images across the \(x\)-axis. The \(x\)-value stays the same.

M (4, 3) M' (4, −3) same x change sign of y

Reflection Across Both Axes

When both signs are flipped, the point reflects across both axes at once, which is the same as a \(180°\) rotation around the origin.

R (3, 4) R' (−3, −4) origin

Comparing Reflection Types

Reflection Rule What Changes Example
Across \(y\)-axis \((x,y) \rightarrow (-x,y)\) Sign of \(x\) \((3,2) \rightarrow (-3,2)\)
Across \(x\)-axis \((x,y) \rightarrow (x,-y)\) Sign of \(y\) \((3,2) \rightarrow (3,-2)\)
Across both \((x,y) \rightarrow (-x,-y)\) Both signs \((3,2) \rightarrow (-3,-2)\)

How to Identify Quadrant and Reflection

1
Look at the signs. Check whether each coordinate is positive or negative.
2
Match signs to quadrant. \((+,+)\) is Q I, \((-,+)\) is Q II, \((-,-)\) is Q III, \((+,-)\) is Q IV.
3
To reflect: To reflect across the \(y\)-axis, flip the sign of \(x\). To reflect across the \(x\)-axis, flip the sign of \(y\).
4
Double-check: the new point should be the same distance from the axis but on the opposite side.

Example 1: Name the Quadrant

What quadrant is the point \((-5, 7)\) in?

x y Q II (−5, 7) −5 7

Example 2: Reflect Across the \(y\)-Axis

Reflect the point \((6, -2)\) across the \(y\)-axis. What is the new point?

(6, −2) (−6, −2) y-axis mirror

Example 3: Reflect Across Both Axes

The point \((-4, 5)\) is reflected across both axes. Where does it land?

(−4, 5) (4, −5) (0, 0) Step A: flip x → (4, 5) Step B: flip y → (4, −5)

Points on an Axis

If one coordinate is zero, the point lies directly on an axis and is not in any quadrant.

On the \(x\)-axis
\(y = 0\): the point is like \((a, 0)\). Example: \((5, 0)\)
On the \(y\)-axis
\(x = 0\): the point is like \((0, b)\). Example: \((0, -3)\)

Common Mistakes to Avoid

✕ Swapping \(x\) and \(y\)
In \((3, -7)\), the first number is always \(x\) (horizontal) and the second is \(y\) (vertical). Mixing them up puts the point in the wrong quadrant.
✕ Flipping the wrong sign
To reflect across the \(y\)-axis, change the sign of \(x\), not \(y\). A common error is flipping the \(y\)-value instead.
✕ Forgetting zero is neither
A point like \((0, 5)\) is on the \(y\)-axis, not in Quadrant I or II. Zero is neither positive nor negative.

Summary: Signs, Quadrants, and Reflections

Quadrant Signs \((x, y)\) Reflect across \(y\) Reflect across \(x\) Reflect across both
I \((+, +)\) Q II Q IV Q III
II \((-, +)\) Q I Q III Q IV
III \((-, -)\) Q IV Q II Q I
IV \((+, -)\) Q III Q I Q II

Question 1 of 5

In which quadrant is the point \((-8, -3)\) located?

Question 2 of 5

The point \((5, 2)\) is reflected across the \(y\)-axis. What are the coordinates of the new point?

Question 3 of 5

Points \((7, -4)\) and \((7, 4)\) are reflections of each other across which axis?

Question 4 of 5

A point is in Quadrant II. Which statement about its coordinates must be true?

Question 5 of 5

The point \((-3, 6)\) is reflected across both axes. What are the coordinates of the image?