Transformations in coordinate geometry are really interesting. They help us understand how shapes move on a graph. There are four main types of transformations: translations, rotations, reflections, and dilations.
A translation moves every point of a shape the same distance in a certain direction.
For example, if we have a triangle with points at (2,3), (4,5), and (3,1), and we move it to the right by 2 units and up by 1 unit, the new points will be at (4,4), (6,6), and (5,2).
Rotations turn a shape around a fixed point, which is called the center of rotation.
For instance, if we rotate a shape 90 degrees clockwise around the origin, the point (x,y) will move to (y,-x).
A reflection flips a shape over a certain line, like the x-axis or y-axis.
For example, if we take the point (2,3) and reflect it over the x-axis, it will become (2,-3).
Dilation changes the size of a shape. It can make it bigger or smaller using a scale factor.
For example, if we have a triangle with points at (1,1), (2,1), and (1,2) and we apply a dilation with a factor of 2, the new points will be (2,2), (4,2), and (2,4).
Seeing these transformations in action helps us think about space better and makes it easier to understand more complicated geometry concepts!
Transformations in coordinate geometry are really interesting. They help us understand how shapes move on a graph. There are four main types of transformations: translations, rotations, reflections, and dilations.
A translation moves every point of a shape the same distance in a certain direction.
For example, if we have a triangle with points at (2,3), (4,5), and (3,1), and we move it to the right by 2 units and up by 1 unit, the new points will be at (4,4), (6,6), and (5,2).
Rotations turn a shape around a fixed point, which is called the center of rotation.
For instance, if we rotate a shape 90 degrees clockwise around the origin, the point (x,y) will move to (y,-x).
A reflection flips a shape over a certain line, like the x-axis or y-axis.
For example, if we take the point (2,3) and reflect it over the x-axis, it will become (2,-3).
Dilation changes the size of a shape. It can make it bigger or smaller using a scale factor.
For example, if we have a triangle with points at (1,1), (2,1), and (1,2) and we apply a dilation with a factor of 2, the new points will be (2,2), (4,2), and (2,4).
Seeing these transformations in action helps us think about space better and makes it easier to understand more complicated geometry concepts!