Rectangle WXYZ with vertices W(1,5), X(7,5), Y(7, 2), and Z(1, 2):
(a) Rotation: 270° counterclockwise
(b) Translation: (x, y) =(x-7, y + 3)
W"( , )
X"( , )
Y"( , )
Z"( , )

First we need to solve for X.

Solve for xx.

-3x+3y=12−3x+3y=12

Divide both sides by -3−3.

x-y=-\frac{12}{3}x−y=−

Simplify \frac{12}{3}

x-y=-4x−y=−4

Add y to both sides.

x=-4+yx=−4+y

Regroup terms.

x=y-4x=y−4

Step two:

Let's start with the normal equation.

3x+6y=-573x+6y=−57

Let x=y-4x=y−4.

3(y-4)+6y=-573(y−4)+6y=−57

Simplify.

9y-12=-579y−12=−57

Great! Now we are on step 3.

Solve for y.

9y-12=-579y−12=−57

Add 1212 to both sides.

9y=-57+129y=−57+12

Simplify -57+12−57+12 to -45−45.

9y=-459y=−45

Divide both sides by 99.

y=-\frac{45}{9}y=−

Simplify \frac{45}{9}  to 55.

y=-5y=−5

Step 4! Boom!!

Now let's start with what we have.

x=y-4x=y−4

Let y=-5y=−5.

x=-5-4x=−5−4

Simplify.

x=-9x=−9

Then our answers are:

x=−9

y=-5y=−5

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