Translating a Triangle

Pre-Algebra · Axiom Academy

EXAMPLE Translating a Triangle Move a shape on the coordinate plane while its size and shape stay exactly the same. Triangle ABC has vertices , , and . Translate the triangle 3 units right and 2 units up , and find the coordinates of the image A'B'C' . Original and Image on the Coordinate Plane Every vertex slides the same way — 3 right, 2 up. Work the algebra below to confirm each new point. Nice work — you translated a whole triangle one vertex at a time. Here's what to remember: A translation is one rule for every point: "3 right, 2 up" becomes , applied identically to A , B , and C . Add to each coordinate: right/left changes x ( +3 ), up/down changes y ( +2 ) — don't swap them. Size and shape are preserved: sliding a figure never changes side lengths or angles, so A'B'C' is congruent to ABC . It's a rigid motion: translation is one of the rigid transformations (with reflections and rotations) — the image is identical to the original except for position. Try the same triangle with a different rule — say — to see how the direction of the slide changes which coordinate goes up or down.

This is the written version of the interactive lesson above. See the full Pre-Algebra course.