Question Video: Identifying a Geometric Transformation Applied to a Quadrilateral | Nagwa Question Video: Identifying a Geometric Transformation Applied to a Quadrilateral | Nagwa

Question Video: Identifying a Geometric Transformation Applied to a Quadrilateral Mathematics

What type of geometrical transformation has been applied to the quadrilateral 𝐴𝐵𝐶𝐷?

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Video Transcript

What type of geometrical transformation has been applied to the quadrilateral 𝐴𝐵𝐶𝐷?

We’re asked to determine what type of transformation has been applied to the given quadrilateral. We need to treat 𝐴𝐵𝐶𝐷 as the object and 𝐴 prime 𝐵 prime 𝐶 prime 𝐷 prime as its image following transformation. The types of transformation we need to consider are translation, rotation, and reflection. And in order to determine which of these has been applied, let’s consider the properties of the object and its image.

First, we can see that all corresponding vertices are in the same position on both shapes. Starting in the lower-left corner, the vertices on both are labeled in alphabetical order in the counterclockwise direction. We can also see that the object and its image are the same size and in the same orientation. This means that the transformation applied cannot be a rotation or a reflection, as for each of these, the object and its image would not be in the same orientation.

In the case of a reflection, the clockwise or counterclockwise labeling of the vertices would also not be preserved. In fact, the only thing that has changed is the position of the shape. Each vertex has moved the same distance in the same direction, which corresponds to a translation. So, we can conclude that the type of geometrical transformation that has been applied to the quadrilateral 𝐴𝐵𝐶𝐷 is a translation.

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