Title: Lesson 6-8
Author: mark_cameron
Last saved by: Glencoe Mathematics
Company: McGraw-Hill

Lesson 6-7

Example 1 Draw a Translation
Copy quadrilateral ABCD below on graph paper. Then draw the image of the figure after a translation of 3 units left and 4 units down.

Step 1	 Move each vertex of the quadrilateral 
 3 units left and 4 units down.

Step 2	 Connect the new vertices to form the image. 

Example 2 Translation in the Coordinate Plane
Graph ΔLMN with vertices L(−4, 4), M(−1, 4), and N(−2, 1). Then graph the image of ΔLMN after a translation of 3 units right and 4 units down. Write the coordinates of its vertices.

The coordinates of the vertices of the image are L′(−1, 0), M′(2, 0), and N′(1, −3). Notice that these vertices can also be found by adding 3 to the x-coordinates and –4 to the y-coordinates, or (3, −4).
	Original		Add (3, −4)			Image
	L(−4, 4)	→	(−4 + 3, 4 + (−4))	→	L′(−1, 0)
	M(−1, 4)	→	(−1 + 3, 4 + (−4))	→	M′(2, 0)
N(−2, 1)	→	(−2 + 3, 1 + (−4))	→	N′(1, −3)

Example 3
STANDARDIZED TEST PRACTICE EXAMPLE 
If triangle ABC is translated 5 units right and 2 units down, what are the coordinates of point B′?

A  (4, 1)		C  (2, –4)
B  (1, 0)		D  (3, 2)

Read the Test Item
You are asked to find the coordinates of point B′ after the original figure has been translated 5 units right and 2 units down. 

Solve the Test Item
You can answer this question without translating the entire triangle.

The coordinates of point B are (–1, 3).		Original figure

The x-coordinate of B is –1, so the			Translating 5 units right is the same
x-coordinate of B′ is –1 + 5 or 4.			as adding 5 to the x-coordinate.

The y-coordinate of B is 3, so the			Translating 2 units down is the same
y-coordinate of B′ is 3 – 2 or 1.			as subtracting 2 from the y-coordinate.

The coordinates of B′ are (4, 1).

The answer is A.