main idea/vocabulary translation graph translations on a coordinate plane

• translation

• Graph translations on a coordinate plane.

http://glencoe.mcgraw-hill.com/sites/0078740509/

Draw a Translation

Copy ΔEFG below on graph paper. Then draw the image of the figure after a translation of 3 units right and 2 units up.

Step 1 Move each vertex of the triangle 3 units right and 2 units up.

Answer:

Step 2 Connect the new vertices to form the image.


1. A

2. B

3. C

4. D0% 0%0%0%

Draw the image of ΔABC after a translation of 2 units right and 4 units down.

A. B.

C. D.


Translation in the Coordinate Plane

Graph ΔABC with vertices A(–2, 2), B(3, 4), and C(4, 1). Then graph the image of ΔABC after a translation of 2 units left and 5 units down. Write the coordinates of its vertices.



The coordinates of the vertices of the image are A'(–4, –3), B'(1, –1), and C'(2, –4). Notice that these vertices can also be found by adding –2 to the x-coordinates and –5 to the y-coordinates, or (–2, –5).



Original Add (–2, –5). Image

A(–2, 2) (–2 + (–2), 2 + (–5)) (–4, –3)

B(3, 4) (3 + (–2), 4 + (–5)) (1, –1)

C(4, 1) (4 + (–2), 1 + (–5)) (2, –4)

Answer: A'(–4, –3), B'(1, –1), and C'(2, –4)


1. A

2. B

3. C

4. D0% 0%0%0%

Graph ΔPQR with vertices P(–1, 3), Q(2, 4), and R(3, 2). Then graph the image of ΔPQR after a translation of 2 units right and 3 units down. Write the coordinates of its vertices.

A. P'(–1, 0), Q'(–4, 1), and R'(–5, 1)

B. P'(1, 0), Q'(4, 1), and R'(5, –1)

C. P'(–1, 0), Q'(–4, –1), and R'(–5, –1)

D. P'(1, 0), Q'(4, –1), and R'(–5, –1)


A. (0, 3) B. (1, 2)

C. (2, 1) D. (1, 1)

If triangle RST is translated 4 units to the right and 3 units up, what are the coordinates of point T' ?


Read the Item

You are asked to find the coordinates of point T' after the original figure has been translated 4 units right and 3 units up.

Solve the Item

You can answer this question without translating the entire triangle.


Original figure

The coordinates of T' are (1, 2).

Answer: The answer is B.

Translating 3 units up is the same as adding 3 to the y-coordinate.

Translating 4 units right is the same as adding 4 to the x-coordinate.

The coordinates of point T are (–3, –1).

The x-coordinate of T is –3, so the x-coordinate of T' is –3 + 4 or 1.

The y-coordinate of T is –1, so the y-coordinate of T' is –1 + 3 or 2.


1. A

2. B

3. C

4. D0% 0%0%0%A. (0, –1)B. (–3, 2)

C. (–1, –4) D. (–2, 3)

If triangle LMN is translated 4 units left and 2 units up, what are the coordinates of point L'?


1. A

2. B

3. C

4. D

0% 0%0%0%

A. x-axis

B. y-axis

C. y = x

D. y = –x

Name the line of reflection for the pair of figures in the picture.

(over Lesson 6-6)

1. A

2. B

3. C

4. D0% 0%0%0%

A. Q'(1, 1), R'(4, –3), S'(–2, –3)

B. Q'(–1, 1), R'(4, –3), S'(–2, 3)

C. Q'(1, –1), R'(4, –3), S'(–2, –3)

D. Q'(–1, –1), R'(4, –3), S'(2, –3)

Find the coordinates of the vertices of ΔQRS with vertices Q(1, 1), R(4, 3), and S(–2, 3) after a reflection over the x-axis.

(over Lesson 6-6)

1. A

2. B

3. C

4. D0% 0%0%0%

A. Square WXYZ was reflected over the x-axis.

B. Square WXYZ was reflected over the y-axis.

C. Square WXYZ was reflected over the line y = x.

D. Square WXYZ was reflected over the line y = –x.

Square WXYZ has vertices W(1, 2), X(1, 4), Y(3, 4), and Z(3, 2). If W'X'Y'Z' has vertices W'(–1, 2), X'(–1, 4), Y'(–3, 4), and Z'(–3, 2), describe the reflection performed on square WXYZ.

(over Lesson 6-6)

main idea/vocabulary translation graph translations on a coordinate plane

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