Ctrl+k

Translate figures on a coordinate plane

A translation moves every point of a figure the same distance in the same direction, preserving side lengths, angle measures, size, and shape. On a coordinate plane, the movement is represented by adding a horizontal and vertical shift to each ordered pair, such as (x,y)→(x+a,y+b)(x,y)\rightarrow(x+a,y+b), with positive and negative values indicating direction; this level focuses on translations of figures using integer-coordinate shifts, not more advanced vector or non-integer treatments.

Detailed Explanation: Translate figures on a coordinate plane

A translation slides a figure without turning or resizing it. Every point moves the same number of units horizontally and vertically.

The rule

(x,y)→(x+a,y+b)(x,y)\rightarrow(x+a,y+b)

means:

  • Add aa to the xx-coordinate to move left or right.
  • Add bb to the yy-coordinate to move up or down.
  • A positive number means right or up.
  • A negative number means left or down.

Example: Translate triangle ABCABC with vertices

A(1,2),B(4,2),C(2,5)A(1,2),\quad B(4,2),\quad C(2,5)

using the rule

(x,y)→(x−3,y+4).(x,y)\rightarrow(x-3,y+4).

This means move every point 33 units left and 44 units up.

Apply the rule to each vertex:

A(1,2)→(1−3,2+4)=(−2,6),B(4,2)→(4−3,2+4)=(1,6),C(2,5)→(2−3,5+4)=(−1,9).\begin{aligned} A(1,2)&\rightarrow(1-3,2+4)=(-2,6),\\ B(4,2)&\rightarrow(4-3,2+4)=(1,6),\\ C(2,5)&\rightarrow(2-3,5+4)=(-1,9). \end{aligned}

So the translated triangle has vertices

A′(−2,6),B′(1,6),C′(−1,9).A'(-2,6),\quad B'(1,6),\quad C'(-1,9).

To check your work, make sure the same horizontal and vertical changes were used for every point. The triangle keeps the same side lengths, angles, size, and shape; it has only moved.

Learn by doing: Translate figures on a coordinate plane

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

    Practice with unlimited practice problems

    Cartesian Grid - Translation of Shape in Two Dimensions (Words)

      ?