Which solid can be represented as a three dimensional figure using the given figure and vector?
a.
cuboid
b.
trapezoid
c.
cone
d.
rectangle
Solution:
A square is given. So, a rectangular prism can be formed from it.
A translation vector indicating 2 units right and 2 units down is given.
Translate each vertex 2 units to the right and 2 units down.
Connect the points to form a three dimensional figure.
The figure represents a cuboid.
Correct answer : (1)
2.
The figure M'N'O'P' is the image of MNOP. Describe the translation vector by using ordered pair notation.
a.
<-14, 8>
b.
<8, 8>
c.
<- 14, 14>
d.
<-8, 8>
Solution:
Identify the coordinates of the MNOP and M'N'O'P'.
The coordinates of MNOP are M(- 3, 3), N(- 1, 5), O(6, 4) and P(2, - 2).
The coordinates of M'N'O'P' are M'(- 11, 11), N'(- 9, 13), O'(- 2, 12) and P'(1, - 6).
Coordinates of image - Coordinates of preimage = Coordinates of the translation vector.
The translation that maps M to M' is (-11 - (- 3), 11 - 3) = (- 8, 8)
Horizontal translation in left direction results in negative x-coordinate and translation in right direction results in positive x-coordinate.
Vertical translation in upward direction results in positive y-coordinate and translation in downward direction results in negative y-coordinate.
The translation is 8 units left and 8 units up.
Hence the translation vector that maps PQRS to P'Q'R'S' is <- 8, 8>.
Correct answer : (4)
3.
Identify the pattern which is not created by translation.
a.
Figure 4
b.
Figure 1
c.
Figure 3
d.
Figure 2
Solution:
A translation is a transformation that moves points the same distance and in the same direction.
The pattern 1 is formed by moving a single figure the same distance and in the same direction. So, it is a translation.
The pattern 2 is also formed by moving a single figure the same distance and in the same direction. So, it is a translation.
The pattern 3 is formed by rotating a single figure. So, it is not a pattern created by translation.
The pattern 4 is also formed by moving a single figure the same distance and in the same direction. So, it is a translation.
Hence pattern in figure 3 is not created by translation.
Correct answer : (3)
4.
The figure M'N'O'P' is the image of MNOP. Describe the vector by using ordered pair notation.
a.
<7, 7>
b.
<- 3, - 7>
c.
<7, 5>
d.
<3, 7>
Solution:
The coordinates of M are (5, 6).
The coordinates of M' are (2, - 1).
The movement in left direction results in negative x-coordinate and the movement in right direction results in positive x-coordinate.
The movement in downward direction results in negative y-coordinate and the movement in upward direction results in positive y-coordinate.
Coordinates of preimage + Coordinates of translation = Coordinates of the image.
The translation vector is <2 - 5, - 1 - 6> = < - 3, - 7> [Coordinates of image - Coordinates of preimage = Coordinates of the translation vector.]
Hence the translation vector is < - 3, - 7>.
Correct answer : (2)
5.
Which solid can be represented as a three dimensional picture using the figure and vector?
a.
pyramid
b.
sphere
c.
cylinder
d.
circle
Solution:
A circle is given. So, a cylinder can be formed from it.
Translate each vertex 1 unit to the right and 5 units down.
Connect the points to form a cylinder.
Correct answer : (3)
6.
Find the single transformation that has the same effect as composition of translations. <3, 7> followed by <11, - 6> followed by <- 8, 3>
a.
<5, 11>
b.
<7, 4>
c.
<-6, -4>
d.
<6, 4>
Solution:
A translation is a transformation that moves points the same distance and in the same direction.
The first translation is <3, 7>.
The second translation is <11, - 6>.
The third translation is <- 8, 3>.
The single transformation which is equivalent to the three translations obtained by adding all the three translations.
The single transformation is <3 + 11 - 8, 7 - 6 + 3> = <6, 4>
Correct answer : (4)
7.
Find the image of A after a translation of <- 2, - 6>.
a.
B
b.
E
c.
D
d.
C
Solution:
The coordinates of A are (4, 4).
The translation vector is <- 2, - 6>.
Coordinates of preimage + Coordinates of translation = Coordinates of the image
The coordinates of A after translation are (4 + (- 2), 4 + (- 6)) = (2, -2)
Hence the image of circle A after translation is represented in circle D.
Correct answer : (3)
8.
On what does a vector quantity depend?
a.
momentum and isolation of a vector
b.
isolation of vector
c.
momentum of vector
d.
distance and direction
Solution:
The distance and direction of a translation is expressed as a vector.
Hence the vector quantity depends on the distance and the direction.
Correct answer : (4)
9.
Identify the incorrect statement. I. A translation is a transformation that moves points the same distance and in the same direction II. A translation is an isometry III. A translation changes the shape and the size of the figure IV. A translation does not change orientation
a.
III
b.
II
c.
IV
d.
I
Solution:
A translation is a transformation that moves points the same distance and in the same direction.
A translation is an isometry.
A translation does not change shape and size of the figure.
A translation does not change orientation.
Hence the statement III is incorrect.
Correct answer : (1)
10.
Find the image of the polygon ABCD under the translation of <0, -5> followed by <-1, -2> using matrix addition.
a.
MNOP
b.
GFEH
c.
KJIL
d.
SRQT
Solution:
Identify the vertices of the polygon ABCD.
The vertices of the pre-image are A(1, 3), B(3, 2), C(4, 3) and D(3, 4).
The vertices of the pre-image in matrix form
A
B
C
D
(1 3 4 33 2 3 4)
The first translation vector is <0, -5>.
The translation vector in matrix form is (0 0 0 0-5 -5 -5 -5)
Vertices of the image = Vertices of pre-image + Translation matrix.