Question

Triangle XYZ undergoes a transformation to form triangle X'Y'Z'. The type of transformation is a

a. Translation
b. Rotation
c. Reflection
d. Dilation

Answer 1

Triangle XYZ undergoes a transformation to form triangle X'Y'Z'. The type of transformation is a dilation

Therefore, correct answer is d. Dilation

Step-by-step explanation:

The transformation described, from triangle XYZ to X'Y'Z', indicates a dilation. Dilation involves scaling an object, either enlarging or reducing it, while maintaining the same shape. Each point in the original triangle XYZ moves outward or inward from the center of dilation to form the new triangle X'Y'Z', with distances proportional but not necessarily equal.

Understanding different geometric transformations is fundamental in geometry and mathematics. Dilation, in particular, plays a crucial role in changing the size of figures while preserving their shape. It is commonly used in various applications, including map scaling and computer graphics.

Therefore, correct answer is d. Dilation

Answer 2

The type of transformation undergone by triangle XYZ to form triangle X'Y'Z' is c. Reflection.

Step-by-step explanation:

In a reflection, each point of the original figure is mirrored across a line, creating a symmetrical image. To identify the type of transformation, we can examine the relationship between corresponding points in the original and transformed triangles. If the corresponding points are equidistant from the line of reflection, a reflection has occurred.

In a reflection, the distance from a point to the line of reflection is preserved. Let's denote the vertices of the original triangle as X[sub]1[/sub]Y[sub]1[/sub]Z[sub]1[/sub], and the corresponding vertices of the transformed triangle as X[sub]1'[/sub]Y[sub]1'[/sub]Z[sub]1'[/sub]. If the distance from X[sub]1[/sub] to the line of reflection is equal to the distance from X[sub]1'[/sub] to the same line, and similarly for Y and Z, then it confirms a reflection. This holds true for all corresponding points.

Therefore, by examining the distances between corresponding points and the line of reflection, we can conclusively determine that the transformation is a reflection.

Understanding geometric transformations is essential for solving problems in geometry and is a fundamental concept in mathematics. Reflections, along with translations, rotations, and dilations, are key tools in studying the properties and relationships of geometric figures.

Therefore, the correct option is c. Reflection