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📐 Translating and Reflecting on the Coordinate Plane

Plot points with (x, y) pairs, then move whole shapes around the grid — slide them with translations and flip them with reflections.

lessons

~15 min

to learn

🔢 Math

subject

Ages 6–12

level

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What you’ll learn

Points on the GridPlot and read points on the coordinate plane using ordered pairs and identify the four quadrants.The coordinate plane is a grid made from two number lines: the x-axis across and the y-axis up, meeting at the origin (0, 0). Each point has an address written (x, y) — go across first, then up. The axes split the plane into four quadrants, and the signs of x and y tell you which corner a point falls in.
Sliding and FlippingTranslate shapes by adding to coordinates and reflect them across the x-axis and y-axis.A translation slides a shape to a new spot without turning or flipping it — add the same amount to every point's x and y. A reflection flips a shape across a mirror line into a mirror image: over the x-axis (x, y) becomes (x, −y), and over the y-axis it becomes (−x, y). Both moves keep the shape congruent, the same size and shape.

Questions this course answers

What is the special point where the x-axis and y-axis cross?

The axes cross at the origin, whose coordinates are (0, 0).

In the ordered pair (4, 7), what does the 4 tell you to do?

In (x, y) the first number is x, which tells you how far to move across.

A point has a negative x and a positive y. Which quadrant is it in?

Negative x means left of the origin and positive y means above it, so the point is in the top-left quadrant.

How is a translation different from a reflection?

A translation slides the shape to a new spot while keeping it facing the same way, unlike a reflection which flips it.

Translate the point (2, 1) right 3 and up 2. Where does it land?

Add 3 to the x and 2 to the y: (2 + 3, 1 + 2) gives (5, 3).

Reflect the point (3, 2) over the x-axis. What is its mirror image?

Reflecting over the x-axis flips the point up-to-down, so only the y-coordinate switches sign: (3, −2).

Grounded in trusted sources

Khan Academy — coordinate plane and transformations
National Council of Teachers of Mathematics
Britannica Kids
BBC Bitesize — coordinates

Every Wunder lesson is built from real, reputable sources — never invented.

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