Translate figures on a coordinate plane

A translation moves every point of a figure the same horizontal and vertical distance, represented on the coordinate plane by $(x,y)\rightarrow(x+a,y+b)$ , where $a$ and $b$ indicate signed coordinate changes. The learner interprets ordered pairs, applies the rule to vertices, and understands that translations preserve lengths, angle measures, orientation, and shape while changing location; formal matrix methods and more advanced transformation compositions are outside this scope.

Detailed Explanation: Translate figures on a coordinate plane

A translation slides a figure without turning it, flipping it, or changing its size.

The rule

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

means:

Add $a$ to every $x$ -coordinate. This moves the figure horizontally.
Add $b$ to every $y$ -coordinate. This moves the figure vertically.
A positive number moves right or up.
A negative number moves left or down.

Example

Translate triangle $ABC$ with vertices

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

using the rule

(x,y)\rightarrow(x-3,y+2).

Step 1: Identify the coordinate changes

The rule says:

$x-3$ : move every point $3$ units left.
$y+2$ : move every point $2$ units up.

Step 2: Apply the rule to each vertex

For $A(1,2)$ :

(1,2)\rightarrow(1-3,2+2)=(-2,4)

So, $A'=(-2,4)$ .

For $B(4,2)$ :

(4,2)\rightarrow(4-3,2+2)=(1,4)

So, $B'=(1,4)$ .

For $C(2,5)$ :

(2,5)\rightarrow(2-3,5+2)=(-1,7)

So, $C'=(-1,7)$ .

Step 3: State the translated figure

The translated triangle has vertices

A'(-2,4),\quad B'(1,4),\quad C'(-1,7).

Every vertex moved $3$ units left and $2$ units up. The triangle keeps the same side lengths, angle measures, orientation, and shape; only its location changes.

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 (Vector)

Earned ?