Hello friends,Previously we have discussed about properties of rational numbers and now Sketching transformations which sometimes become a tough task and we need a continuous practice and hard work to understand this intersting and a bit complex topic. Here I am going to tell you the best way of understanding Sketching Transformations with geometry help. And this is for grade V of gujarat secondary education board. In basic transformation geometry there is two basic types that are rigid transformations and non-rigid transformations. And also there are three types of rigid transformations known as translations, reflections and rotations. In other words, a transformation is a copy of a geometric figure and copy holds certain properties. Let’s take a simple example when we copy/paste a picture on our computer. Then the original figure is called the pre-image and the new copied picture is called the image of the transformation. The rigid transformation is one in which the pre-image and the image both have same size and shape. In simple word transforms means to change. In geometry, a transformation changes the position of a shape on a coordinate plane. That means shape is moving from one place to another
Translations: - The definition of a translation is every point of the pre-image is moved the same distance in the same direction to form the image. Let’s take an example of triangle each point of triangle is translated or moved 6 inches to the right and 4 inches up.In this case, the rule is 6 to the right and 4 up. You can also translate a pre-image to the any combination of two of the four directions.
The transformation for this example would be T(x, y) = (x+6, y+4).
Reflections: - is a flip of an object over a line. The example of Reflection is given below. This will helps you to understand Reflection.(want to Learn more about Transformations,click here),
Reflection in the coordinate plane over x-axis: - T(x, y) = (x, -y).
Reflection in the coordinate plane over y-axis: - T(x, y) = (-x, y).
Reflection in the coordinate plane over line y = x: - T(x, y) = (y, x).
Rotation: - In rotation (turn) a letter can turn on a point away from its original position. When we watch the T move it turns in place so that it now looks like it is lying on its side and almost look like a clock hand turning around the face of a clock.
Scaling: - Scaling is a linear transformation and the scale factor is the same in all directions. It is also called dilation and the result of uniform scaling is similar to the original.
When one shape can become another using Turns, Flips and/or Slides called Congruent.
Resizing: - The other important Transformation is resizing. In resizing the shape becomes bigger or smaller.
Similar or Congruent: - In Similar or Congruent if one shape become another using transformation, the two shapes might be just similar.
Translation of points: -
A point (p,q) can be moved to another position by applying a column matrix vector.
The column matrix vector is just two numbers, one above the other surrounded by long brackets. The top number adds to the p-coordinate while the bottom number adds to the q-coordinate.
From the above I hope it would help you to understand Sketching transformations, geometry and if anyone want to know about Problem solving strategies and also on Estimating probability then they can refer to internet and text books for understanding it more precisely.
Translations: - The definition of a translation is every point of the pre-image is moved the same distance in the same direction to form the image. Let’s take an example of triangle each point of triangle is translated or moved 6 inches to the right and 4 inches up.In this case, the rule is 6 to the right and 4 up. You can also translate a pre-image to the any combination of two of the four directions.
The transformation for this example would be T(x, y) = (x+6, y+4).
Reflections: - is a flip of an object over a line. The example of Reflection is given below. This will helps you to understand Reflection.(want to Learn more about Transformations,click here),
Reflection in the coordinate plane over x-axis: - T(x, y) = (x, -y).
Reflection in the coordinate plane over y-axis: - T(x, y) = (-x, y).
Reflection in the coordinate plane over line y = x: - T(x, y) = (y, x).
Rotation: - In rotation (turn) a letter can turn on a point away from its original position. When we watch the T move it turns in place so that it now looks like it is lying on its side and almost look like a clock hand turning around the face of a clock.
Scaling: - Scaling is a linear transformation and the scale factor is the same in all directions. It is also called dilation and the result of uniform scaling is similar to the original.
When one shape can become another using Turns, Flips and/or Slides called Congruent.
Resizing: - The other important Transformation is resizing. In resizing the shape becomes bigger or smaller.
Similar or Congruent: - In Similar or Congruent if one shape become another using transformation, the two shapes might be just similar.
Translation of points: -
A point (p,q) can be moved to another position by applying a column matrix vector.
The column matrix vector is just two numbers, one above the other surrounded by long brackets. The top number adds to the p-coordinate while the bottom number adds to the q-coordinate.
From the above I hope it would help you to understand Sketching transformations, geometry and if anyone want to know about Problem solving strategies and also on Estimating probability then they can refer to internet and text books for understanding it more precisely.
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