L4 · Translations and reflections in four quadrants

Learning goal

“I can translate and reflect points and polygons anywhere in the four quadrants, writing the image coordinates, and I can describe a translation or reflection from before-and-after coordinates.”

Transformation — a move that maps a shape to an image: translation, reflection or rotation. The image is congruent to the original.

Translation — a slide: every point moves the same distance in the same direction, written (x + a, y + b).

Reflection — a flip over a mirror line; in this lesson the mirror is the x-axis or the y-axis.

Image — the shape after the transformation; its vertices are written with primes: A' (read "A prime").

Worked example

Triangle with vertices (1, 2), (3, 2), (1, 4) is translated by (x - 4, y - 1): 4 left, 1 down. Step 1: Apply the SAME two changes to every vertex - a translation never treats vertices differently. Step 2: (1, 2) -> (1 - 4, 2 - 1) = (-3, 1). (3, 2) -> (-1, 1). (1, 4) -> (-3, 3). Step 3: The triangle slid from Quadrant I into Quadrant II, unchanged in size, shape and orientation - a slide cannot flip or turn a shape. Say it plainly: one rule, every vertex, signs carried carefully. Most translation errors are sign errors, not idea errors.

Check yourself — explain it

In a translation, all vertices get the same (a, b) added because...

Paired problem — example still visible

Translate (2, -5) by (x + 3, y + 2). -> (5, -3)

Faded completion — last step is yours

"Translate (-2, 3) by (x - 2, y - 4): (-2 - 2, 3 - 4) = ( ___, ___ )" -> (-4, -1)

Ready to practise?

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

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