Question

graph the image of square wxyz after the following sequence of transformations:
rotation 270° counterclockwise around the origin
reflection across the line x = -3

Explanation:

Step1: Find coordinates of original square

Assume \(Z(6,4)\), \(W(10,2)\), \(X(12,6)\), \(Y(10,8)\)

Step2: Apply \(270^{\circ}\) counter - clockwise rotation formula

The formula for a \(270^{\circ}\) counter - clockwise rotation about the origin \((x,y)\to(y, - x)\)

• For \(Z(6,4)\): \(Z'(4,-6)\)
• For \(W(10,2)\): \(W'(2,-10)\)
• For \(X(12,6)\): \(X'(6,-12)\)
• For \(Y(10,8)\): \(Y'(8,-10)\)

Step3: Apply reflection across \(x = - 3\) formula

The formula for reflection across \(x=a\) is \((x,y)\to(2a - x,y)\)
Here \(a=-3\), so \((x,y)\to(-6 - x,y)\)

• For \(Z'(4,-6)\): \(Z''(-6 - 4,-6)=(-10,-6)\)
• For \(W'(2,-10)\): \(W''(-6 - 2,-10)=(-8,-10)\)
• For \(X'(6,-12)\): \(X''(-6 - 6,-12)=(-12,-12)\)
• For \(Y'(8,-10)\): \(Y''(-6 - 8,-10)=(-14,-10)\)

Answer:

Plot the points \(Z''(-10,-6)\), \(W''(-8,-10)\), \(X''(-12,-12)\), \(Y''(-14,-10)\) and connect them to form the image of the square after the given transformations.