Transformations on the Coordinate Plane Worksheet

Transformations on the Coordinate Plane Worksheet
  • Page 1
 1.  
Find the coordinates of C′, if a square ABCD is rotated 180° clockwise around the origin.

a.
(0, 6)
b.
(- 6, - 6)
c.
(0, - 6)
d.
(6, 0)


Solution:

A rotation is a transformation that turns a figure about a fixed point called the center of rotation.


The following figure is obtained when the square ABCD is rotated 180° clockwise around the origin.

The coordinates of C′ are (- 6, - 6).


Correct answer : (2)
 2.  
Find the coordinates of C′, if triangle ABC is rotated 180o counterclockwise around the origin.

a.
(0, - 3)
b.
(- 3, 0)
c.
(0, 3)
d.
(- 3, - 2)


Solution:

A rotation is a transformation that turns a figure about a fixed point called the center of rotation.


The following figure is obtained when the triangle ABC is rotated 180° counterclockwise around the origin.

The coordinates of C′ are (0, - 3).


Correct answer : (1)
 3.  
The point C (4, - 3) is first reflected over x-axis and then reflected over y-axis. What are the coordinates of the final image?
a.
(4, 3)
b.
(4, - 3)
c.
(3, - 4)
d.
(- 4, 3)


Solution:

When a point is reflected over a horizontal line, the x-coordinate remains the same and the sign of the y-coordinate changes.

The coordinates of the point after the reflection on x-axis is (4, 3).

When a point is reflected over a vertical line, the y-coordinate remains the same and the sign of the x-coordinate changes.


The coordinate of the point when reflected over the y-axis is (- 4, 3) as shown in the following figure.

The coordinates of the final image of point C are (- 4, 3).


Correct answer : (4)
 4.  
Point D is located at (5, 3). If you translate the point (x, y) (x - 2, y - 1), then what would be the coordinates of D′?
a.
(3, 4)
b.
(7, 2)
c.
(7, 4)
d.
(3, 2)


Solution:

The rule of trasformaton for the point D at (5, 3) is (x - 2, y - 1).

So, (5 - 2, 3 - 1) = (3, 2)

The coordinates of the point D′ are (3, 2).


Correct answer : (4)
 5.  
ABCD is a quadrilateral with coordinates (3, 1), (6, 1), (5, 4) and (1, 3). It is translated to points A′(- 2, 3), B′( 1, 3), C′(0, 6) and D′(- 4, 5). Find the rule for the translation.
a.
5 units right and 2 units down
b.
2 units left and 2 units up
c.
5 units left and 2 units up
d.
2 units down and 2 units right


Answer: (c)


Correct answer : (3)
 6.  
Find the new coordinates of the figures ABCDE, if you translate 3 units left and 2 units up.


a.
A′(1, 3), B′(5, 7), C′(1, 9), D′(2, 6) E′(-1, 5)
b.
A′(1, 3), B′(5, 7), C′(7, 9), D′(2, 6) E′(-1, 5)
c.
A′(-7, 3), B′(11, 7), C′(1, 9), D′(2, 6) E′(-1, 5)
d.
A′(-7, 3), B′(11, 7), C′(1, 9), D′(8, 6) E′(-1, 5)


Answer: (a)


Correct answer : (1)
 7.  
Triangle ABC has vertices A(4, 4), B(8, 4), C(4, 8). Which graph shows the reflect over the graph y = 3 and then the graph of y = - 2?

a.
Graph 2
b.
Graph 1
c.
Graph 3
d.
Graph 4


Solution:

Graph 2 shows a reflection of triangle ABC over the line y = 3 followed by another reflection over the line y = - 2.
[Only a reflection flips a figure.]


Correct answer : (1)
 8.  
Identify the rule to describe the translation of the triangle ABC to the triangle A′B′C′.


a.
(x, y) (x - 4, y + 3)
b.
(x, y) (x + 4, y + 3)
c.
(x, y) (x + 3, y + 4)
d.
(x, y) (x + 4, y - 3)


Answer: (b)


Correct answer : (2)
 9.  
A translation is also called as _______.
a.
turn
b.
slide
c.
flip
d.
None of the above


Solution:

A translation is also called as slide.


Correct answer : (2)
 10.  
What type of transformation is illustrated in the figure?


a.
Symmetry
b.
Reflection
c.
Translation
d.
Rotation


Solution:

The center of the circle A is moved 5 units down to form the image of the circle with center A'
[From the figure.]

A A'
[Point A goes to point A'.]

So, it is a translation.


Correct answer : (3)

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