Translations — Sliding Points (Grades 6–8)
A translation slides a point a fixed distance in a direction, without turning or flipping it.
Understanding translations on the coordinate plane
Add the slide to each coordinate: moving (2, 3) right 4 and up 1 gives (2 + 4, 3 + 1) = (6, 4). Moving left or down means subtracting (or adding a negative).
Seeing it in action
Worked example
Translate (2, 3) right 4 and up 1.
x: 2 + 4 = 6. y: 3 + 1 = 4. → (6, 4).
Right 4 and up 1 gives (6, 4).
A common mistake, and the fix
Moving the wrong coordinate, or the wrong way.
“Right 4 and up 1” adds 4 to x and 1 to y: (2, 3) becomes (6, 4). Adding the 4 to y instead gives (2, 7), a move straight up. Left and down subtract: (2, 3) moved left 4 is (−2, 3).
Try a few
Translate (1, 1) right 3, up 2
Translate (5, 5) left 2, down 1
Translate (0, 0) right 6, up 6
Coordinate Quest
A calm treasure-map game for plotting, reading, and translating points on a coordinate plane.
Try it in Numeris.
A short lesson, then practice with feedback on every answer.
Put the reasoning on paper.
Try six fraction, angle, perimeter and area questions with explained answers, for grades 4–6.
Free printable · 3 pagesText version (screen-reader friendly): Draw it. Explain it. Math sample
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