How to Graph Translations on the Coordinate Plane?

Step by step guide to Graph Translations on the Coordinate Plane

Translation on the coordinate plane is sliding a point or figure in any direction without any changes in size or shape. In fact, during translation, the coordinates of the vertices of a figure or point change, and they slide left or right, up, or down without changing size or shape.

Translations in a coordinate plane can be described by this coordinate notation: $(x, y)→(x+a, y+b)$, where $a$ and $b$ are constants. Each point shifts $a$ units horizontally and $b$ units vertically. Note that to graph a translation, you should perform the same change for each point.

Translations on the Coordinate Plane – Example 1:

Translate triangle IGH $-2$ units in the $x-$direction and $-3$ units in the $y-$direction.

Solution:

First, write the original coordinates of the points:

$I=(-2, 4)$ $G=(1, 2)$ $H=(4, 3)$

Use this coordinate notation for translating each point: $(x, y)→(x+a, y+b)$

$a=-2$, $b=-3$, then: $(x, y)→(x-2, y-3)$

Then: $I^\prime=(-4, 1)$ $G^\prime=(-1, -1)$ $H^\prime=(2, 0)$

Now, find new points on the coordinate plane and graph the new triangle by $I^\prime, G^\prime, H^\prime$ coordinates.

Translations on the Coordinate Plane – Example 2:

Graph the image of the figure using the transformation given.

Translation:  $4$ units left and $3$ units up.

Solution:

First, write the original coordinates of the points:

$I=(3, 0)$ $G=(2, -4)$ $H=(5, -2)$

Use this coordinate notation for translating each point: $(x, y)→(x+a, y+b)$

$4$ units left →$a=-4$

$3$ units up →$b=3$

Then: $I^\prime=(-1, 3)$ $G^\prime=(-2, -1)$ $H^\prime=(1, 1)$

Now, find new points on the coordinate plane and graph the new triangle by $I^\prime, G^\prime, H^\prime$ coordinates.

Exercises for Translations on the Coordinate Plane

Graph the image of the figure using the transformation given.

1.Translation: $5$ units right and $2$ unit up.

2.Translation: $3$ units left and $5$ unit up.