L8 · Reflections and rotations on the Cartesian plane

Learning goal

“I can reflect a point or polygon over the x-axis or the y-axis and write the coordinate rule, and I can rotate a point or polygon 90°, 180° or 270° about one of its vertices, tracking the coordinates before and after.”

Reflection (on the plane) — a flip over a mirror line - here, the x-axis or the y-axis; the image is a mirror image of the original.

Rotation (on the plane) — a turn of a shape about a fixed point, through a stated angle (90°, 180° or 270°), clockwise unless stated otherwise.

Centre of rotation — the fixed point the shape turns about; in this lesson, always one of the shape's own vertices, which does not move.

Coordinate rule — the instruction that maps every point (x, y) to its image, e.g. reflection over the y-axis: (x, y) -> (-x, y).

Worked example

Point A (2, 3) is reflected over the x-axis, then point B (4, 1) is reflected over the y-axis. Step 1: Reflecting over the x-axis flips the plane up-down. A point's distance from the x-axis is its y-value, so the image sits the same distance on the other side: y becomes -y, and x is unchanged. A (2, 3) -> (2, -3). Rule: (x, y) -> (x, -y). Step 2: Reflecting over the y-axis flips left-right: x becomes -x, y unchanged. B (4, 1) -> (-4, 1). Rule: (x, y) -> (-x, y). Step 3: Name the pattern: the coordinate that names distance FROM the mirror axis is the one that negates. x-axis mirror -> y negates. y-axis mirror -> x negates.

Check yourself — explain it

Reflecting (5, 2) over the x-axis gives...

Paired problem — example still visible

Reflect C (3, 5) over the y-axis. -> (-3, 5)

Faded completion — last step is yours

"Reflect D (6, 4) over the x-axis: D' = ( 6, ___ )" -> (6, -4)

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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