##### Notes

This printable supports Common Core Mathematics Standard HSN-VM.C.12

##### Print Instructions

NOTE: Only your test content will print.
To preview this test, click on the File menu and select Print Preview.

See our guide on How To Change Browser Print Settings to customize headers and footers before printing.

# Matrices and Transforming Geometric Shapes (Grades 11-12)

Print Test (Only the test content will print)

## Matrices and Transforming Geometric Shapes

1.
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. $[[1,0],[0,-1]] \ [[1,1],[2,3],[5,1]]$
2. $[[-1,0],[0,1]] \ [[1,2,5],[1,3,1]]$
3. $[[-1,0],[0,1]] \ [[1,1],[2,3],[5,1]]$
4. $[[1,0],[0,-1]] \ [[1,2,5],[1,3,1]]$
2.
The vertex matrix for rectangle ABCD is $V = [[1,1,4,4],[1,3,3,1]]$. Which of the following is the correct transformed vertex matrix, if the transformation matrix $A = [[0,1],[-1,0]]$ is applied?
1. $[[1,-1],[3,-1],[3,-4],[1,-4]]$
2. $[[-1,-3,-3,-1],[1,1,4,4]]$
3. $[[1,3,3,1],[-1,-1,-4,-4]]$
4. $[[-1,-3,-3,-1],[-1,-1,-4,-4]]$
3.
For the vertex matrix $V = [[1,1,3,3],[-1,2,2,-1]]$ and transformation matrix $M = [[1,2],[0,1]]$, what is the resulting shape if M is applied to V? Choose the most specific classification possible.
1. Square
2. Parallelogram
3. Rectangle
4.
Put the vertices of the shape in the graph below into a vertex matrix, and then apply the rotation matrix $A = [[sqrt(2)/2, -sqrt(2)/2],[sqrt(2)/2, sqrt(2)/2]]$. By what angle, measured in degrees, has the shape been rotated (given that the angle of rotation is counterclockwise)? 1. 30°
2. 45°
3. 60°
4. 105°
5.
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. $[[1,0],[0,1]] [[-1,0],[0,-1]] = [[-1,0],[0,-1]]$
2. $[[1,0],[0,-1]] [[-1,0],[0,1]] = [[0,1],[1,0]]$
3. $[[-1,0],[0,1]] [[1,0],[0,-1]] = [[-1,0],[0,-1]]$
4. $[[1,0],[0,-1]] [[-1,0],[0,1]] = [[-1,0],[0,-1]]$
6.
Which one of the following matrix equations correctly shows the transformation of the first rectangle, whose vertex matrix is $V_1 = [[1,1,4,4],[1,2,2,1]]$, to the second rectangle, whose vertex matrix is $V_2 = [[-4,-4,2,2],[1,3,3,1]] ?$  1. $V_2 = [[2,0],[0,2]] (V_1 - [[1,1,1,1],[1,1,1,1]] ) - [[4,4,4,4],[-1,-1,-1,-1]]$
2. $V_2 = [[2,0],[0,2]] V_1 - [[5,5,5,5],[0,0,0,0]]$
3. $V_2 = [[-4,1/2],[3/2, 1]] V_1$
4. $V_2 = [[2,2],[2,2]] ( V_1 - [[1,1,1,1],[1,1,1,1]])$
7.
For the following questions, let $T = [[2,-2],[0,3]]$ be a transformation matrix. Also, let $V_1 = [[2,5,5,2],[2,2,-1,-1]]$ be the vertex matrix of a square whose area is 9 units squared.
A.
What is the resulting matrix if $V_1$ is transformed by $T$? Let this matrix be $V_2$.
1. $[[0,6,12,6],[6,6,-3,-3]]$
2. $[[0,6,5,2],[6,6,-1,-1]]$
3. $[[2,6,8,2],[0,6,3,-1]]$
4. $[[4,10,10,4],[6,6,-3,-3]]$
B.
What is the area of the resulting shape, defined by the vertex matrix $V_2 ?$
1. 108 units squared
2. 72 units squared
3. 54 units squared
4. 36 units squared
C.
What is the absolute value of the determinant of the transformation matrix, $T ?$
1. 6
2. 7
3. 12
4. 3
D.
How does the absolute value of the determinant of the transformation matrix relate to the area of the two quadrilaterals (the square, $S_1$ and the transformed shape, $S_2$)? Choose the equation which correctly describes this relationship.
1. $|det(T)| = "Area"(S_1) \ "Area"(S_2)$
2. $"Area"(S_2) = |det(T)| \ "Area"(S_1)$
3. $|det(T)| = |"Area"(S_2) - "Area"(S_1)|$
4. There is no relationship between the absolute value of the determinant of T and the area of the shapes.        You need to be a HelpTeaching.com member to access free printables.