When a point (a, b) is rotated 90 counterclockwise about the origin, then the coordinates of the image point will be________.

Therefore, we can say that the Rotation can be done both in clockwise or counter clockwise direction.

Rays drawn from the center of rotation to a point and their image form the __________ of rotation.

The angle of rotation is nothing but the angle between the line that joins center of rotation to the real point and the line that joins the center of rotation and the image point.

Rays drawn from the center of rotation to a point and their image form the __________ of rotation.

The angle of rotation is nothing but the angle between the line that joins center of rotation to the real point and the line that joins the center of rotation and the image point.

It is a transformation in which a figure is rotated around a fixed point called__________.

>>>>The center of rotation is the point that rotates the given figure about a point.

It is a transformation in which a figure is rotated around a fixed point called__________.

>>>>The center of rotation is the point that rotates the given figure about a point.

Use matrix multiplication to find the image. Graph the polygon and its image.
Reflect $open square brackets table row cell negative 4 end cell cell negative 3 end cell cell negative 1 end cell row 0 3 2 end table close square brackets$ in the y-axis.

The required matrix representation is:
$open square brackets table row cell negative 1 end cell 0 row 0 1 end table close square brackets open square brackets table row cell negative 4 end cell cell negative 3 end cell cell negative 1 end cell row 0 3 2 end table close square brackets equals open square brackets table row cell negative 1 left parenthesis negative 4 right parenthesis plus 0 left parenthesis 0 right parenthesis end cell cell negative 1 left parenthesis negative 3 right parenthesis plus 0 left parenthesis 3 right parenthesis end cell cell negative 1 left parenthesis negative 1 right parenthesis plus 0 left parenthesis 2 right parenthesis end cell row cell 0 left parenthesis negative 4 right parenthesis plus left parenthesis 1 right parenthesis 0 end cell cell 0 left parenthesis negative 3 right parenthesis plus left parenthesis 1 right parenthesis left parenthesis 3 right parenthesis end cell cell 0 left parenthesis negative 1 right parenthesis plus left parenthesis 1 right parenthesis left parenthesis 2 right parenthesis end cell end table close square brackets equals open square brackets table attributes columnalign left end attributes row 4 3 1 row 0 3 2 end table close square brackets$

Use matrix multiplication to find the image. Graph the polygon and its image.
Reflect $open square brackets table row cell negative 4 end cell cell negative 3 end cell cell negative 1 end cell row 0 3 2 end table close square brackets$ in the y-axis.

Use matrix multiplication to find the image. Graph the polygon and its image.
Reflect $open square brackets table row cell negative 4 end cell cell negative 3 end cell cell negative 1 end cell row 0 3 2 end table close square brackets$ in the x-axis.

Therefore, the required matrix is:
$open square brackets table row 1 0 row 0 cell negative 1 end cell end table close square brackets open square brackets table row cell negative 4 end cell cell negative 3 end cell cell negative 1 end cell row 0 3 2 end table close square brackets equals open square brackets table row cell 1 left parenthesis negative 4 right parenthesis plus 0 left parenthesis 0 right parenthesis end cell cell 1 left parenthesis negative 3 right parenthesis plus 0 left parenthesis 3 right parenthesis end cell cell 1 left parenthesis negative 1 right parenthesis plus 0 left parenthesis 2 right parenthesis end cell row cell 0 left parenthesis negative 4 right parenthesis plus left parenthesis negative 1 right parenthesis 0 end cell cell 0 left parenthesis negative 3 right parenthesis plus left parenthesis negative 1 right parenthesis left parenthesis 3 right parenthesis end cell cell 0 left parenthesis negative 1 right parenthesis plus left parenthesis negative 1 right parenthesis left parenthesis 2 right parenthesis end cell end table close square brackets equals open square brackets table row cell negative 4 end cell cell negative 3 end cell cell negative 1 end cell row 0 cell negative 3 end cell cell negative 2 end cell end table close square brackets$

Use matrix multiplication to find the image. Graph the polygon and its image.
Reflect $open square brackets table row cell negative 4 end cell cell negative 3 end cell cell negative 1 end cell row 0 3 2 end table close square brackets$ in the x-axis.

Coordinate Geometry: This is one of The branches of geometry in which a point's position is defined using coordinates.
Coordinates: Coordinates are a set of values that help to determine the exact location of a point in the coordinate plane.
Coordinate Plane: The two-dimensional plane formed by intersecting two perpendicular lines, the x-axis, and y-axis, is known as Coordinate Plane.
Distance Formula: The distance is used to calculate the length between two points in A(x₁,y₁) and B(x₂,y₂).
Section Formula: It is used to divide any line into two parts in an m:n ratio.
Mid-Point Theorem: Mid-Point Theorem formula determines the coordinates at which a line is divided into two halves.

Find point C on the x-axis, so AC + BC is minimum.
A(3, 4), B (-3, 6)

¶Coordinate Geometry Terms
¶

Coordinate Geometry: This is one of The branches of geometry in which a point's position is defined using coordinates.
Coordinates: Coordinates are a set of values that help to determine the exact location of a point in the coordinate plane.
Coordinate Plane: The two-dimensional plane formed by intersecting two perpendicular lines, the x-axis, and y-axis, is known as Coordinate Plane.
Distance Formula: The distance is used to calculate the length between two points in A(x₁,y₁) and B(x₂,y₂).
Section Formula: It is used to divide any line into two parts in an m:n ratio.
Mid-Point Theorem: Mid-Point Theorem formula determines the coordinates at which a line is divided into two halves.

What is the line of reflection for $triangle A B C$ and its image?

From the graph, the line of reflection is x-axis.

What is the line of reflection for $triangle A B C$ and its image?

From the graph, the line of reflection is x-axis.

What is the line of reflection for $triangle A B C$ and its image?

From the graph, the line of reflection is y = x.

What is the line of reflection for $triangle A B C$ and its image?

From the graph, the line of reflection is y = x.

The matrix $open square brackets table row 1 0 row 0 cell negative 1 end cell end table close square brackets$ show the reflection in

The reflection matrix in the x-axis = $open square brackets table row 1 0 row 0 cell negative 1 end cell end table close square brackets$

The matrix $open square brackets table row 1 0 row 0 cell negative 1 end cell end table close square brackets$ show the reflection in

The reflection matrix in the x-axis = $open square brackets table row 1 0 row 0 cell negative 1 end cell end table close square brackets$

The matrix $open square brackets table row cell negative 1 end cell 0 row 0 1 end table close square brackets$ show the reflection in

* The reflection matrix in the y-axis = $open square brackets table row cell negative 1 end cell 0 row 0 1 end table close square brackets$

The matrix $open square brackets table row cell negative 1 end cell 0 row 0 1 end table close square brackets$ show the reflection in

* The reflection matrix in the y-axis = $open square brackets table row cell negative 1 end cell 0 row 0 1 end table close square brackets$

Write the matrix for the polygon.

The required matrix is:
$space space space space A space space space space B space space C space space space space space D open square brackets table row cell negative 3 end cell 1 cell negative 2 end cell cell negative 4 end cell row 2 cell negative 1 end cell cell negative 2 end cell cell negative 1 end cell end table close square brackets$

Write the matrix for the polygon.

Write the matrix for the polygon.

The required matrix is:
$space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space A B C M a t r i x space o f space t h e space p o l y g o n space equals open square brackets table row cell negative 6 end cell cell negative 5 end cell cell negative 3 end cell row cell negative 4 end cell cell negative 1 end cell cell negative 2 end cell end table close square brackets$

Write the matrix for the polygon.

Use matrix multiplication to find the image. Graph the polygon and its image.
Reflect $open square brackets table attributes columnalign center center right center end attributes row 2 6 5 2 row cell negative 2 end cell cell negative 3 end cell cell negative 8 end cell cell negative 5 end cell end table close square brackets$ in the y-axis.

The required matrix for the image is:
$open square brackets table row cell negative 1 end cell 0 row 0 1 end table close square brackets open square brackets table row 2 6 5 2 row cell negative 2 end cell cell negative 3 end cell cell negative 8 end cell cell negative 5 end cell end table close square brackets equals open square brackets table row cell left parenthesis negative 1 right parenthesis left parenthesis 2 right parenthesis plus 0 left parenthesis negative 2 right parenthesis end cell cell left parenthesis negative 1 right parenthesis left parenthesis 6 right parenthesis plus 0 left parenthesis negative 3 right parenthesis end cell cell left parenthesis negative 1 right parenthesis left parenthesis 5 right parenthesis plus 0 left parenthesis negative 8 right parenthesis end cell cell left parenthesis negative 1 right parenthesis left parenthesis 2 right parenthesis plus 0 left parenthesis negative 5 right parenthesis end cell row cell 0 left parenthesis 2 right parenthesis plus 1 left parenthesis negative 2 right parenthesis end cell cell 0 left parenthesis 6 right parenthesis plus 1 left parenthesis negative 3 right parenthesis end cell cell 0 left parenthesis 5 right parenthesis plus 1 left parenthesis negative 8 right parenthesis end cell cell 0 left parenthesis 2 right parenthesis plus 1 left parenthesis negative 5 right parenthesis end cell end table close square brackets equals open square brackets table attributes columnalign center center right left end attributes row cell negative 2 end cell cell negative 6 end cell cell negative 5 end cell cell negative 2 end cell row cell negative 2 end cell cell negative 3 end cell cell negative 8 end cell cell negative 5 end cell end table close square brackets$

Use matrix multiplication to find the image. Graph the polygon and its image.
Reflect $open square brackets table attributes columnalign center center right center end attributes row 2 6 5 2 row cell negative 2 end cell cell negative 3 end cell cell negative 8 end cell cell negative 5 end cell end table close square brackets$ in the y-axis.

Use matrix multiplication to find the image. Graph the polygon and its image.
Reflect $open square brackets table attributes columnalign center center right center end attributes row 2 6 5 2 row cell negative 2 end cell cell negative 3 end cell cell negative 8 end cell cell negative 5 end cell end table close square brackets$ in the x-axis.

The matrix representation of the image :
$open square brackets table row 1 0 row 0 cell negative 1 end cell end table close square brackets open square brackets table row 2 6 5 2 row cell negative 2 end cell cell negative 3 end cell cell negative 8 end cell cell negative 5 end cell end table close square brackets equals open square brackets table row cell 1 left parenthesis 2 right parenthesis plus 0 left parenthesis negative 2 right parenthesis end cell cell 1 left parenthesis 6 right parenthesis plus 0 left parenthesis negative 3 right parenthesis end cell cell 1 left parenthesis 5 right parenthesis plus 0 left parenthesis negative 8 right parenthesis end cell cell 1 left parenthesis 2 right parenthesis plus 0 left parenthesis negative 5 right parenthesis end cell row cell 0 left parenthesis 2 right parenthesis plus left parenthesis negative 1 right parenthesis left parenthesis negative 2 right parenthesis end cell cell 0 left parenthesis 6 right parenthesis plus left parenthesis negative 1 right parenthesis left parenthesis negative 3 right parenthesis end cell cell 0 left parenthesis 5 right parenthesis plus left parenthesis negative 1 right parenthesis left parenthesis negative 8 right parenthesis end cell cell 0 left parenthesis 2 right parenthesis plus left parenthesis negative 1 right parenthesis left parenthesis negative 5 right parenthesis end cell end table close square brackets equals open square brackets table attributes columnalign center center right left end attributes row 2 6 5 2 row cell negative 2 end cell cell negative 3 end cell cell negative 8 end cell cell negative 5 end cell end table close square brackets$

Use matrix multiplication to find the image. Graph the polygon and its image.
Reflect $open square brackets table attributes columnalign center center right center end attributes row 2 6 5 2 row cell negative 2 end cell cell negative 3 end cell cell negative 8 end cell cell negative 5 end cell end table close square brackets$ in the x-axis.