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) |

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 180^{o} counterclockwise around the origin.

a. | (0, - 3) | ||

b. | (- 3, 0) | ||

c. | (0, 3) | ||

d. | (- 3, - 2) |

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) |

The coordinates of the point after the reflection on

When a point is reflected over a vertical line, the

The coordinate of the point when reflected over the

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 ($x$, $y$) $\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) |

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 |

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) |

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 |

[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. | ($x$, $y$) $\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) |

Correct answer : (2)

9.

A translation is also called as _______.

a. | turn | ||

b. | slide | ||

c. | flip | ||

d. | None of the above |

Correct answer : (2)

10.

What type of transformation is illustrated in the figure?

a. | Symmetry | ||

b. | Reflection | ||

c. | Translation | ||

d. | Rotation |

[From the figure.]

A

[Point A goes to point A'.]

So, it is a translation.

Correct answer : (3)