What is the orientation of a figure

Transformations

Objective

In this lesson, we’ll explore transformations, which are changes to the size, shape, location, or orientation of a figure.

Table of Contents Show

Transformations
Transformations
How do you find the orientation of a figure?
What is an orientation of an object?
What changes the orientation of a figure?
How do you describe orientation?

Previously Covered

In the previous lesson we reviewed a few properties of polygons.

Transformations

Let’s investigate three types of transformations: translations, reflections, and rotations.

Translation

A figure undergoes a translation when it slides a certain distance in a certain direction. The translated figure is called the image of the original figure. It is congruent to the original figure.

The yellow figure (M) has been translated a distance of 9.00 cm to the right. The orange figure (J) is the translated image of the yellow figure (M).

Reflection

A reflection is a transformation that produces a mirror image of the original figure by flipping it across a line. While the reflection changes the object’s orientation (top and bottom, left and right), the reflected image is congruent to the original figure.

The yellow figure (left) has been reflected over the dotted line to produce the orange mirror image (right).

The image below shows a figure that has a property called bilateral symmetry. The figure can be divided in half by a line of symmetry so that one side is a mirror image of the other side. In fact, this figure has many lines of symmetry, but only one is drawn here. All regular polygons have bilateral symmetry.

Bilateral Symmetry

Rotation

A rotation is a transformation that rotates an object around a point. While the rotation changes the object’s orientation, the rotated image is congruent to the original figure.

The yellow figure has been rotated 215° around point A to produce the orange figure.

The equilateral triangle below has a property called rotational symmetry. A figure has this property if it can be rotated around a point by less than 360° and the object appears unchanged. This figure can be rotated 120° or 240° and it will appear unchanged.

Polygon with Rotational Symmetry

Question

Which of these is an example of a translation?

Reveal Answer

The correct answer is B. A translation is a transformation that slides a figure a certain distance in a certain direction. Choice A shows rotation, which rotates a figure around a given point. Choice C shows a reflection, which produces a mirror image of a figure over a line. Choice D doesn’t show anything.

Review

Transformations are changes to the size, shape, location, or orientation of a figure.
Translation occurs when a figure is moved a certain distance in a certain direction.
Reflection produces a mirror image of the original figure.
Rotation moves an object around a point.

Reflection does not preserve orientation.
Dilation (scaling), rotation and translation (shift) do preserve it.

Perfect example of "oriented" figure on a plane is the right triangle #Delta ABC# with sides #AB=5#, #BC=3# and #AC=4#.

To introduce orientation, let's position ourselves above the plane and, looking down on this triangle, notice that the way from vertex #A# to #B# and then to #C# can be viewed as the clockwise movement.

Rotation, translation (shift) or dilation (scaling) won't change the fact that the direction #A->B->C# is clockwise.

Use now a reflection of this triangle relative to some axis. For instance, reflect it relative to a line #BC#. This transformation will leave vertices #B# and #C# in place (that is, #B'=B# and #C'=C#), but vertex #A# from being to the left of line #BC# will move to the right of it to a new point #A'#.

The way #A'->B->C# is counterclockwise. That is a manifestation of (1) our triangle has orientation and (2) the transformation of reflection does not preserve the orientation.

How do you find the orientation of a figure?

The following are true about orientation of a figure: It is determined by how the figure appears on the plane including the position of the vertices of the figure. It does not require the labeling of vertices to make a determination. It is preserved during these transformations: translations and dilations.

What is an orientation of an object?

In geometry, the orientation, angular position, attitude, bearing, or direction of an object such as a line, plane or rigid body is part of the description of how it is placed in the space it occupies.

What changes the orientation of a figure?

Rotation. A rotation is a transformation that rotates an object around a point. While the rotation changes the object's orientation, the rotated image is congruent to the original figure.

How do you describe orientation?

Orientation definition Orientation refers to a process of introducing new employees to the company and assimilating them with its policies, benefits and culture. It's the first step in employee's continuous socialization process.