The Translation Rule

Part of the Transformations & Constructions section of Coddy's Geometry journey. Lesson 3 of 60.

G(2, 1) moves to G'(-3, 3). That is 5 steps left and 2 steps up. Every point moves the same way, so one line can describe them all.

$(x,\ y) \to (x - 5,\ y + 2)$

Test it on H(5, 1): $5-5 = 0$ and $1+2 = 3$ , so H goes to (0, 3). That point is H'. This line is the rule of the translation. The translation $\langle a,\ b \rangle$ has the rule $(x,\ y) \to (x + a,\ y + b)$ .

$Triangle GHJ and its image, moved 5 left and 2 up$

Challenge

Triangle ABC and its image are on the grid. Write the rule that moves ABC onto its image. Use the form (x + a, y + b).

Then press Check.

Try it yourself

$Move the shape onto its target$

Move the shape onto its target

All lessons in Transformations & Constructions

1Translations

Sliding a Shape Draw the ImageThe Translation RuleRecap: Translations

4Combining Moves

One Move, Then Another Order Matters Two Mirrors Name the Move Recap: Combining Moves

7Drawing on Squared Paper

Lengths by Pythagoras Perpendicular Steps Squares by Area Right Triangles by Area Midpoints on the Grid Recap: Squared Paper

10Perpendiculars and Parallels

Perpendicular From a Point Perpendicular at a Point Parallel Through a Point Tools You Have Earned Recap: Parallels