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Common Core Standard HSN-VM.C.12 Questions

(+) Work with 2 × 2 matrices as a transformations of the plane, and interpret the absolute value of the determinant in terms of area.

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Grade 12 Matrices CCSS: HSN-VM.C.12
Given the triangle with vertices (1,1),(2,3), and (5,1), which of the following matrix expressions would represent the reflection of this triangle over the y-axis?
  1. [100-1] [112351]
  2. [-1001] [125131]
  3. [-1001] [112351]
  4. [100-1] [125131]
Grade 12 Matrices CCSS: HSN-VM.C.12
The vertex matrix for rectangle ABCD is V=[11441331]. Which of the following is the correct transformed vertex matrix, if the transformation matrix A=[01-10] is applied?
  1. [1-13-13-41-4]
  2. [-1-3-3-11144]
  3. [1331-1-1-4-4]
  4. [-1-3-3-1-1-1-4-4]
Grade 12 Matrices CCSS: HSN-VM.C.12
Which of the following equations correctly state that, for a figure in the cartesian plane, a reflection over the x-axis, followed by a reflection over the y-axis, is identical to a 180° rotation (either clockwise or counterclockwise)?
  1. [1001][-100-1]=[-100-1]
  2. [100-1][-1001]=[0110]
  3. [-1001][100-1]=[-100-1]
  4. [100-1][-1001]=[-100-1]
Grade 12 Matrices CCSS: HSN-VM.C.12
Which one of the following matrix equations correctly shows the transformation of the first rectangle, whose vertex matrix is V1=[11441221], to the second rectangle, whose vertex matrix is V2=[-4-4221331]?
1x3 Q1 Horizontal
2x6 Q2 Horizontal
  1. V2=[2002](V1-[11111111])-[4444-1-1-1-1]
  2. V2=[2002]V1-[55550000]
  3. V2=[-412321]V1
  4. V2=[2222](V1-[11111111])
Grade 12 Matrices CCSS: HSN-VM.C.12

This question is a part of a group with common instructions. View group »

How does the absolute value of the determinant of the transformation matrix relate to the area of the two quadrilaterals (the square, S1 and the transformed shape, S2)? Choose the equation which correctly describes this relationship.
  1. |det(T)|=Area(S1) Area(S2)
  2. Area(S2)=|det(T)| Area(S1)
  3. |det(T)|=|Area(S2)-Area(S1)|
  4. There is no relationship between the absolute value of the determinant of T and the area of the shapes.
Grade 12 Matrices CCSS: HSN-VM.C.12

This question is a part of a group with common instructions. View group »

What is the resulting matrix if V1 is transformed by T? Let this matrix be V2.
  1. [0612666-3-3]
  2. [065266-1-1]
  3. [2682063-1]
  4. [41010466-3-3]
Grade 12 Matrices CCSS: HSN-VM.C.12

This question is a part of a group with common instructions. View group »

What is the area of the resulting shape, defined by the vertex matrix V2?
  1. 108 units squared
  2. 72 units squared
  3. 54 units squared
  4. 36 units squared
Grade 12 Matrices CCSS: HSN-VM.C.12

This question is a part of a group with common instructions. View group »

What is the absolute value of the determinant of the transformation matrix, T?
  1. 6
  2. 7
  3. 12
  4. 3
Grade 12 Matrices CCSS: HSN-VM.C.12
Which matrix could be used to find the area of a parallelogram with the coordinates (0,0),(5,7),(2,1),(7,8)?
  1. [5877]
  2. [5778]
  3. [5127]
  4. [5721]

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