Mathematics
Grade9
Easy

Question

Write the matrix for the polygon.

  1. space space space space A space space B space space space space C space space space space D
open square brackets table row cell negative 3 end cell 0 cell negative 2 end cell cell negative 5 end cell row 5 4 cell negative 1 end cell 2 end table close square brackets
  2. space space space space A space space space space space B space space space space space C space space space space space space D
open square brackets table row cell negative 3 end cell 0 cell negative 2 end cell cell negative 5 end cell row 5 cell negative 4 end cell 1 2 end table close square brackets
  3. space space space space A space space space space B space space space space C space space space space D
open square brackets table row cell negative 3 end cell 0 cell negative 2 end cell cell negative 5 end cell row cell negative 5 end cell 4 1 2 end table close square brackets
  4. space space space space A space space space B space space space space C space space space space D
open square brackets table row cell negative 3 end cell 0 cell negative 2 end cell cell negative 5 end cell row 5 4 1 2 end table close square brackets

hintHint:

Representing every vertices of a polygon in the columns gives the matrix of a polygon.

The correct answer is: space space space space A space space space B space space space space C space space space space D
open square brackets table row cell negative 3 end cell 0 cell negative 2 end cell cell negative 5 end cell row 5 4 1 2 end table close square brackets


    * In Geometry, a reflection is known as a flip. A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection.
    *It is a type of transformation that produces mirror image of the shape.
    * Matrix representation is the efficient way for the transformation of points.
    * Every vertex is placed in columns.
    Given That:

    *From figure
    :                   The coordinates of the polygon are A(-3, 5), B(0, 4), C(-2, 1), and D(-5, 2).
    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 space space space space space A space space space B space space C space space space space D
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 3 end cell 0 cell negative 2 end cell cell negative 5 end cell row 5 4 1 2 end table close square brackets

    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 space space space space space A space space space B space space C space space space space D
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 3 end cell 0 cell negative 2 end cell cell negative 5 end cell row 5 4 1 2 end table close square brackets

    Related Questions to study

    Grade9
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    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 space space A space B space 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 attributes columnalign left end attributes row 2 6 7 row 4 1 5 end table close square brackets

    Write the matrix for the polygon.

    MathematicsGrade9

    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 space space A space B space 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 attributes columnalign left end attributes row 2 6 7 row 4 1 5 end table close square brackets

    Grade9
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    Use matrix multiplication to find the image. Graph the polygon and its image. Reflect  open square brackets table attributes columnalign left end attributes row 1 3 4 row 2 3 0 end table close square brackets in the y - axis.

    The required matrix is:
    open square brackets table row cell negative 1 end cell 0 row 0 1 end table close square brackets open square brackets table attributes columnalign left end attributes row 1 3 4 row 2 3 0 end table close square brackets equals open square brackets table row cell negative 1 left parenthesis 1 right parenthesis plus 0 left parenthesis 2 right parenthesis end cell cell negative 1 left parenthesis 3 right parenthesis plus 0 left parenthesis 3 right parenthesis end cell cell negative 1 left parenthesis 4 right parenthesis plus 0 left parenthesis 0 right parenthesis end cell row cell 0 left parenthesis 1 right parenthesis plus 1 left parenthesis 2 right parenthesis end cell cell 0 left parenthesis 3 right parenthesis plus 1 left parenthesis 3 right parenthesis end cell cell 0 left parenthesis 4 right parenthesis plus 1 left parenthesis 0 right parenthesis end cell end table close square brackets equals open square brackets table row cell negative 1 end cell cell negative 3 end cell cell negative 4 end cell row 2 3 0 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 left end attributes row 1 3 4 row 2 3 0 end table close square brackets in the y - axis.

    MathematicsGrade9

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

    Grade9
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    Use matrix multiplication to find the image. Graph the polygon and its image. Reflect
    open square brackets table attributes columnalign left end attributes row 1 3 4 row 2 3 0 end table close square brackets in the x - axis.

    >>>Since, it is reflected on x-axis, the matrix multiplication looks like:
    open square brackets table row 1 0 row 0 cell negative 1 end cell end table close square brackets open square brackets table attributes columnalign left end attributes row 1 3 4 row 2 3 0 end table close square brackets equals open square brackets table row cell 1 left parenthesis 1 right parenthesis plus 0 left parenthesis 2 right parenthesis end cell cell 1 left parenthesis 3 right parenthesis plus 0 left parenthesis 3 right parenthesis end cell cell 1 left parenthesis 4 right parenthesis plus 0 left parenthesis 0 right parenthesis end cell row cell 0 left parenthesis 1 right parenthesis plus left parenthesis negative 1 right parenthesis 2 end cell cell 0 left parenthesis 3 right parenthesis plus left parenthesis negative 1 right parenthesis left parenthesis 3 right parenthesis end cell cell 0 left parenthesis 4 right parenthesis plus left parenthesis negative 1 right parenthesis left parenthesis 0 right parenthesis end cell end table close square brackets equals open square brackets table row 1 3 4 row cell negative 2 end cell cell negative 3 end cell 0 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 left end attributes row 1 3 4 row 2 3 0 end table close square brackets in the x - axis.

    MathematicsGrade9

    >>>Since, it is reflected on x-axis, the matrix multiplication looks like:
    open square brackets table row 1 0 row 0 cell negative 1 end cell end table close square brackets open square brackets table attributes columnalign left end attributes row 1 3 4 row 2 3 0 end table close square brackets equals open square brackets table row cell 1 left parenthesis 1 right parenthesis plus 0 left parenthesis 2 right parenthesis end cell cell 1 left parenthesis 3 right parenthesis plus 0 left parenthesis 3 right parenthesis end cell cell 1 left parenthesis 4 right parenthesis plus 0 left parenthesis 0 right parenthesis end cell row cell 0 left parenthesis 1 right parenthesis plus left parenthesis negative 1 right parenthesis 2 end cell cell 0 left parenthesis 3 right parenthesis plus left parenthesis negative 1 right parenthesis left parenthesis 3 right parenthesis end cell cell 0 left parenthesis 4 right parenthesis plus left parenthesis negative 1 right parenthesis left parenthesis 0 right parenthesis end cell end table close square brackets equals open square brackets table row 1 3 4 row cell negative 2 end cell cell negative 3 end cell 0 end table close square brackets

    parallel
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    Find point C on the x-axis, so AC + BC is minimum.
    A(4, -3), B (8, -5)

    >>>Finding A'B line AB' line intersection point gives the point that gives minimum sum of AC and BC on x-axis.
    >>>Therefore, the point of intersection becomes: C(5.5,0).

    Find point C on the x-axis, so AC + BC is minimum.
    A(4, -3), B (8, -5)

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    >>>Finding A'B line AB' line intersection point gives the point that gives minimum sum of AC and BC on x-axis.
    >>>Therefore, the point of intersection becomes: C(5.5,0).

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    Find point C on the x-axis, so AC + BC is minimum.
    A(2, 4), B (6, 2)

    The point present in the x-axis. and also on the line image of A and point B.
    >>>From the given data the point  becomes (4.7,0)

    Find point C on the x-axis, so AC + BC is minimum.
    A(2, 4), B (6, 2)

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    The point present in the x-axis. and also on the line image of A and point B.
    >>>From the given data the point  becomes (4.7,0)

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

    From the graph, the line of reflection is x= -1

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

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    From the graph, the line of reflection is x= -1

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

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

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

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

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    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?

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

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    Find the reflection matrix on the x-axis.

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

    Find the reflection matrix on the x-axis.

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

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    Write the matrix for the polygon.

    From the graph, the coordinates of polygon are A(0, 2), B(0, 4), C(3, 5), and D(3, 1)
    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 space B space C space D
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 attributes columnalign left end attributes row 0 0 3 3 row 2 4 5 1 end table close square brackets

    Write the matrix for the polygon.

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    From the graph, the coordinates of polygon are A(0, 2), B(0, 4), C(3, 5), and D(3, 1)
    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 space B space C space D
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 attributes columnalign left end attributes row 0 0 3 3 row 2 4 5 1 end table close square brackets

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    Find the image coordinates of the triangle ABC, if A (-4,0), B (-3,3) and C (-1,2), which is reflected along y-axis.

    If (a, b) is reflected in the y-axis, its image is the point (-a, b).
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    A (-4, 0)  → A’ (4, 0)
    B (-3, 3) → B’ (3, 3)
    C (-1, 2) → C’ (1, 2)
    Image coordinates of the triangle ABC are A’ (4, 0), B’ (3, 3) and C’ (1, 2).

    Find the image coordinates of the triangle ABC, if A (-4,0), B (-3,3) and C (-1,2), which is reflected along y-axis.

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    If (a, b) is reflected in the y-axis, its image is the point (-a, b).
    (a, b) → (-a, b)
    A (-4, 0)  → A’ (4, 0)
    B (-3, 3) → B’ (3, 3)
    C (-1, 2) → C’ (1, 2)
    Image coordinates of the triangle ABC are A’ (4, 0), B’ (3, 3) and C’ (1, 2).

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    Find the image coordinates of the line AB, if A (6, 4) and B (6,1), which is reflected along y = -x

    If (a, b) is reflected in the line y = -x, its image is the point (-b, -a).
    (a, b) → (b, a)
    A(6, 4) → A’(-4, -6)
    B (6,1) → B’(-1, -6)
    Image of the line A’( -4, -6), B’( -1, -6)

    Find the image coordinates of the line AB, if A (6, 4) and B (6,1), which is reflected along y = -x

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    If (a, b) is reflected in the line y = -x, its image is the point (-b, -a).
    (a, b) → (b, a)
    A(6, 4) → A’(-4, -6)
    B (6,1) → B’(-1, -6)
    Image of the line A’( -4, -6), B’( -1, -6)

    parallel
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    Find the image coordinates of the line AB, if A (6, 4) and B (6, 1), which is reflected along y = x

    If (a, b) is reflected in the line y = x, its image is the point (b, a).
    (a, b) → (b, a)
    A (6, 4) → A’ (4, 6)
    B (6, 1) → B’ (1, 6)
    Image of line A’ (4, 6), B’ (1, 6)

    Find the image coordinates of the line AB, if A (6, 4) and B (6, 1), which is reflected along y = x

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    If (a, b) is reflected in the line y = x, its image is the point (b, a).
    (a, b) → (b, a)
    A (6, 4) → A’ (4, 6)
    B (6, 1) → B’ (1, 6)
    Image of line A’ (4, 6), B’ (1, 6)

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    Graph the reflection of the polygon in the given line: y = -x

    If (a, b) is reflected in the line y = -x, its image is the point (-b, -a).
    (a, b) → (-b, -a)
    A (-6, -4)  → (4, 6)
    B (-5, -1) → (1, 5)
    C (-3, -2) → (2, 3)

    Graph the reflection of the polygon in the given line: y = -x

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    If (a, b) is reflected in the line y = -x, its image is the point (-b, -a).
    (a, b) → (-b, -a)
    A (-6, -4)  → (4, 6)
    B (-5, -1) → (1, 5)
    C (-3, -2) → (2, 3)

    Grade9
    Mathematics

    Graph the reflection of the polygon in the given line: y = x

    If (a, b) is reflected in the line y = x, its image is the point (b, a).
    (a, b) → (b, a)
    A (-6, -4)  → (-4, -6)
    B (-5, -1) → ( -1, -5)
    C (-3, -2) → (-2, -3)

    Graph the reflection of the polygon in the given line: y = x

    MathematicsGrade9

    If (a, b) is reflected in the line y = x, its image is the point (b, a).
    (a, b) → (b, a)
    A (-6, -4)  → (-4, -6)
    B (-5, -1) → ( -1, -5)
    C (-3, -2) → (-2, -3)

    parallel

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