# 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).

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).

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).

4.
Point D is located at (5, 3). If you translate the point ($x$, $y$) $\to$ ($x$ - 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).

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

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)

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.]

8.
Identify the rule to describe the translation of the triangle ABC to the triangle A′B′C′.

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

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.

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.