91Ó°ÊÓ

Explain how you know that \((3,-3)\) is a solution of the system \(x-3 y=12\) and \(2 x+y=3 .\)

Explain how you can determine whether a dilation is a reduction or an enlargement.

Write a system of equations that has \((0,1)\) as a solution.

Describe two techniques for finding the rotation of a figure about a fixed point.

Suppose you reflect a figure over the \(x\)-axis and then reflect that image over the \(y\)-axis. Is this double reflection the same as a translation? Explain why or why not.

a. Graph the system of equations. $$ \begin{aligned} &y=x+5 \\ &2 y=2 x+10 \end{aligned} $$ b. List five solutions. c. Make a conjecture about systems of equations in part a.

Manuel says that if a figure with parallel sides is reflected over the \(x\)-axis, the reflected figure will also have parallel sides. Natalie says that such a reflected figure may not always have parallel sides. Who is correct? Explain why.

Describe the difference between the substitution and elimination methods. Explain when it is better to use each method.

Write about dilations that you can find in everyday life. Explain whether they are reductions or enlargements and estimate what the scale factors might be.

Diem rotated quadrilateral HIJK \(305^{\circ}\) in a clockwise direction about the origin. Lakesha said she could have rotated the quadrilateral \(55^{\circ}\) in a counterclockwise direction and found the same image. Is Lakesha correct? Explain why or why not.