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What are Transformations?

Transformations of a figure are changed in the image or the way the figured is presented. Methods to transform figures are translation, rotation, reflection and enlargement.

Sliding down on a sliding board or moving an object, this motion is an example of translation. Translation is moving a figure from one place to another. A translation moves all points in a plane the same distance and in the same directions. A vector indicates the distance and direction of the glide.

ΔABC from the original position will move to ΔA’B’C’ from X to X’. Vector is XX’ indicates the distance and direction of glide. Translation satisfy the conditions that points are moves in the same direction.

Looking in the mirror or any shiny surface, you can see your reflection. An object and its reflected image are one of the geometric transformations called reflection. Reflection appears to be in back as the object is in front. An object transforms into a reflection object and its images are always the same perpendicular distance. Observe the figure.

The triangle is reflected by a mirror line (red line). The line in dash shows the similar vertices of a triangle to another triangle. However, even without the dash lines in the vertices, the angles and segment length can identify that the triangle is reflected.

Rotations involve all turning motions like turning a doorknob or winding a tape measure on the reel. A transformation is a rotation if the centre and an angle of rotation are given. The rotation can be counterclockwise or clockwise.

In a circle with point B, move counterclockwise. If the rotation of an angle is counterclockwise then it is a positive angle. If rotated clockwise, then it is a negative angle. The centre of rotation is point A. Since it forms a radius, even if it moves around the circumference of the circle it is still equidistant.

Note: In rotation the point and the figure are always same in distance.

Enlargement is increasing the size of an object or figure. The important state of enlargement is the scale and the centre of enlargement. The scale factor is the range of the figure that will expand. It indicates how many times a given object increase its size. Centre of enlargement is a fixed point inside or outside the figure to expand.

Steps in Enlargement:
a. From the point of centre, if enlargement, draw lines connecting to the vertices of the figure to enlarge.
b. Measure the lengths of each line.
c. If the scale factor is 2, from the line of the centre of enlargement, double the length. If the scale factor is 3, draw lines three times as long.