Translations

Geometry · Axiom Academy

Sliding shapes on the coordinate plane A translation slides every point of a figure by the same amount. To translate a point (x, y) by a units horizontally and b units vertically, you add the shift to each coordinate. where a is the horizontal shift and b is the vertical shift The signs of a and b tell you which way the figure slides. Horizontal shift first, vertical shift second: Here a triangle is translated by (4, 2) — each point moves right 4 and up 2. The dashed blue triangle is the pre-image ; the solid green one is the image . Watch all three vertices ride parallel arrows of the same length — that's what "same distance, same direction" looks like. The same translation can be written three equivalent ways. Pick whichever is clearest for the problem. The animation adds the vector to a point tail-to-tip — the move all three notations describe. shows exactly how the coordinates change the subscript (a,b) is the translation vector the "direction and distance" of the slide 5. Example 1 — Translating a Point Translate point P(2, 5) by the vector . Watch P ride the vector across the grid, then check the arithmetic below. 6. Example 2 — Translating a Triangle Triangle ABC has vertices A(-2, 1) , B(3, 1) , and C(0, 4) . Find the image after the translation . Watch all three vertices slide left 4 and up 2 in lock-step, then read off each new coordinate below. 7. Example 3 — Finding the Translation Point Q(1, -3) is translated to Q'(7, 2) . What translation was applied?

This is the written version of the interactive lesson above. See the full Geometry course.