remains the same. When an object is reflected about a mirror line, - PowerPoint PPT Presentation

D AY 12 – IDENTIFYING RIGID MOTIONS

I NTRODUCTION When an object is moved from one place to another, its original position changes but the shape and size remains the same. When an object is reflected about a mirror line, it remains at its original position and an image forms on the opposite side of the mirror. Having this in mind among with others, in situations where, the pre-image and the image are given, we can identify a rigid motion that can relate the two. In this topic, we are going to discuss how we can identify the type of rigid motion given two objects.

V OCABULARY Line of symmetry – It is an imaginary line where you can fold an object or image and have two equal and overlapping parts.

 Reflection  To identify a reflection we check whether there can be a line of symmetry between the two objects.  In the figure above a line of symmetry can be identified between them. Thus the rigid motion is a reflection

 Translation  To identify whether a rigid motion is a translation, we check whether the object has been moved to a certain distance and that the object’s shape, size and orientation remains the same after being moved.  In the figure above the two triangles are equal in size, shape and their orientations are the same. Thus the rigid motion involved is translation.

Glide reflection To identify a glide reflection we check whether one object appears to be a reflection of the other which has been moved by a certain distance. B B Rectangle B above appears be are a reflection of A which was moved to the right.

Rotation To identify a rotation we have to check whether a fixed point can be identified. To do so, we connect at least three lines of an object point with its corresponding image point. When the perpendicular bisector meets at common point, the image would be as a result of rotation.

y 14 12 10 8 6 4 2 0 x 4 8 12 6 10 2

 A fixed point can be identified at (6,1) and the distance from the object to the fix point remains the same as the distance from the image to the fixed point.  Connecting at least three lines of an object point with its corresponding image point, then drawing their perpendicular bisectors, we find that they meet at common point, (6,1) .

HOMEWORK  Identify the rigid motion involved in the set up below.

A NSWERS TO HOMEWORK 1.Translation

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