Question

figure u is the result of a transformation on figure t. which transformation would accomplish that? answer a translation 2 units left and 3 units down a translation 3 units left and 2 units down a rotation 90° counterclockwise about the origin a rotation 90° clockwise about the origin

Explanation:

Step1: Analyze translation

Translation moves the figure without rotation. If we consider translation, the orientation of Figure \(U\) relative to Figure \(T\) is not just a simple shift. For example, if we assume a translation, the angles and the relative position of the vertices in terms of direction (not just \(x - y\) shift) do not match a pure translation.

Step2: Analyze rotation

Rotation changes the orientation of the figure.

• For a \(90^{\circ}\) counter - clockwise rotation about the origin \((x,y)\to(-y,x)\).
• For a \(90^{\circ}\) clockwise rotation about the origin \((x,y)\to(y, - x)\).

If we take a point from Figure \(T\), say a vertex \((x,y)\) and apply a \(90^{\circ}\) clockwise rotation about the origin.
Let's assume a non - origin vertex of Figure \(T\) (for simplicity, assume a point \((1,2)\) in a general sense of the figure's coordinate). After a \(90^{\circ}\) clockwise rotation about the origin, it becomes \((2,-1)\) which is in line with the transformation from Figure \(T\) to Figure \(U\) (by checking the overall orientation and position of the vertices of the two figures in the coordinate - plane).

Answer:

A rotation \(90^{\circ}\) clockwise about the origin.