Geometric Transformation: Reflection
**
A. Basic Competencies
3.5 Explain geometric transformations (reflection, translation, rotation and dilation) which is connected to contextual problems.4.5 Resolve contextual problems related to geometric transformation (reflection, translation, rotation and dilation)
B. Learning Objectives
After studying the Geometry Transformation material, you are expected to be able to:
Explain geometric transformations (reflection, translation, rotation and dilation) which is connected to contextual problems.
Resolve contextual problems related to geometric transformation (reflection, translation, rotation and dilation)
C. Material
Transformation is a process that changes the position or shape of an object. Mathematically, transformation of a flat object means moving or mapping all points on an object to other places on the same plane. There are transformations that change the position of objects/buildings, but their shape and size are the same as before the transformation. There are also transformations that change the position and size of the object/shape being transformed even though the shape is still the same. The type of transformation we will study is mirroring (reflection), shift (translation), rotation (rotation), and multiplication (dilatation).
Reflection
Reflection or mirroring is a type of transformation that moves each point on a plane (or geometric shapes) by using the properties of the object and its image in a plane mirror. Look at the image below:
Do you remember looking in the mirror? When you approach the mirror, it appears that your reflection will also approach the mirror. When you move away from the mirror, your image will also move away from the mirror. The characteristics of the image of an object formed by mirroring include the following. - The reflected image of a shape has the same shape and size as the original shape. - The distance of the image to the mirror is the same as the distance of the original object to the mirror. - The image of the shape in the mirror is opposite to the original shape.**
Various reflections
**
1. Reflection on the x-axis
Example: Look for the reflection of point A(-2, 3) to the x-axisSolution:Look at the following picture:
2. Reflection on the y-axis
Example: Look for the reflection of point A(-2, 3) towards the y-axisSolution:Look at the following picture:
3. Reflection on the line y = x
Example: Look for the reflection of point A(-2, 3) to line y = xSolution:Look at the following picture:
4. Reflection on the line y = -x
Example: Look for the reflection of point A(-2, 3) to line y = -xSolution:Look at the following picture:
Below we provide a simulation of the reflection of triangle ABC on the x-axis, please try it.
Based on the examples above, the reflection results of a point can be concluded as presented in the following table:**
**
| Axis Line | Starting Point | Shadow | Example |
|---|---|---|---|
| x-axis | A (x,y) | A' (x, -y) | A (-2, 3) Become A' (-2, -3) |
| y-axis | A (x,y) | A' (-x,y) | A (-2, 3) Become A' (2, 3) |
| Line y = x | A (x,y) | A' (y, x) | A (-2, 3) Become A' (3, -2) |
| Line y = -x | A (x,y) | A' (-y, -x) | A (-2, 3) Become A' (-3, 2) |
D. Evaluation
After studying the geometric transformation material in the reflection sub-material, we now carry out an evaluation to find out our understanding of this reflection material. Please do the following quiz:
This is the geometric transformation material in the reflection submaterial. I hope this is helpful. 😊🙏
