Exercise 38 Page 550

Use the vector P⟨ 4,1 ⟩ to form a translation rule. Then use the translation on the preimages and compare the expression with the images.

x=1, w=3, y=0, z=2/3

Practice makes perfect

To find the variables, we should find the translation rule between the preimages and the images. The vector P⟨ 4,1 ⟩ translates a point 4 units to the right on the x-axis and 1 unit up on the y-axis giving us the following translation. ccc (x,y) & → & (x+4,y+1) [0.5em] A(- 1,w) & → & A'(3,w+1) B(8y-1,1) & → & B'(8y+3,2)Since we already have coordinates for A' and B', we can create four equations. We can then use these equations to solve for each variable.

After Translation	Image	Equate x-coordinates	Equate y-coodinates
A'(3,w+1)	A'(2x+1,4)	3=2x+1	w+1=4
B'(8y+3,2)	B'(3,3z)	8y+3=3	2=3z

Now we can solve each equation by isolating the variables.

Equation	Solution	Equation	Solution
3=2x+1	x=1	w+1=4	w=3
8y+3=3	y=0	2=3z	z=2/3

The values of the variables are x=1, w=3, y=0 and z= 23.

Subchapter links

Communicate Your Answer p.543

Monitoring Progress p.545-547

Exercises p.548-550

Exercise 38 Page 550

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