Coordinates in four quadrants
Locate points and describe reflections using the signs of their coordinates.
Before you begin
- Positive and negative numbers
- Perpendicular horizontal and vertical axes
Travel horizontally, then vertically
An ordered pair (x, y) names a position relative to the origin. Move x units along the horizontal direction and y units vertically. Positive x points right and positive y points up. Each quadrant has a sign pattern: upper right is (+,+), upper left is (−,+), lower left is (−,−), and lower right is (+,−). Points on an axis are not in a quadrant.
Use sign changes to describe a reflection
Reflecting across the horizontal x-axis preserves the horizontal position and reverses the vertical position, giving (x, −y). Reflecting across the y-axis gives (−x, y). Reflecting across both axes reverses both signs. Fractions and decimals are located using the same rule; first check what distance one tick mark represents on each axis.
Worked example
Locate A = (−3, 2), then reflect it across the y-axis.
Show the worked solution
- Move three units left and two units up from the origin to locate A in quadrant II.
- A reflection across the y-axis keeps the height 2 and reverses the horizontal position.
- The reflected point is three units right and two units up.
A′ = (3, 2), in quadrant I.
Try it yourself
Where is (0, −4)?
Common mistakes
- The coordinate order is x first, then y.
- A reflection in an axis changes the coordinate perpendicular to that axis.
What can you explain now?
Reflect (2.5, −1) across the x-axis, then across the y-axis.
Compare with the explanation
(2.5, 1), then (−2.5, 1).
The first reflection changes only the y-coordinate. The second changes only the x-coordinate.
After trying it yourself, choose your next review. This is your self-assessment.
Your review choice appears on Today. Sign in to sync it across devices.
Original StudyForA content. AI-assisted checks completed; subject-teacher review is still pending. These lessons are not endorsed by an exam board.
Common Core mathematics standards ↗