Question

question figure u is the result of a transformation on figure t. which transformation would accomplish this? answer a translation 5 units to the left and 3 units up a rotation 90° clockwise about the origin a rotation 90° counterclockwise about the origin a rotation 180° counterclockwise about the origin

Explanation:

Step1: Analyze translation

Translation moves the figure without rotation. Figure \(U\) is rotated compared to Figure \(T\), so "A translation 5 units to the left and 3 units up" is wrong.

Step2: Analyze rotation rules

• For a point \((x,y)\) rotated \(90^{\circ}\) clockwise about the origin, the new coordinates are \((y, -x)\).
• For a point \((x,y)\) rotated \(90^{\circ}\) counter - clockwise about the origin, the new coordinates are \((-y,x)\).
• For a point \((x,y)\) rotated \(180^{\circ}\) counter - clockwise about the origin, the new coordinates are \((-x,-y)\).

Let's assume a point on Figure \(T\) (say \((- 4,-2)\)).

• If we rotate \((-4,-2)\) \(90^{\circ}\) clockwise about the origin: using the formula \((y, -x)\), we get \((-2,4)\) (not matching).
• If we rotate \((-4,-2)\) \(90^{\circ}\) counter - clockwise about the origin: using the formula \((-y,x)\), we get \((2,-4)\) (not matching).
• If we rotate \((-4,-2)\) \(180^{\circ}\) counter - clockwise about the origin: using the formula \((-x,-y)\), we get \((4,2)\) (not the right transformation).

Let's use another approach. Visually, a \(90^{\circ}\) clockwise rotation about the origin changes the orientation of the figure in a way that matches the transformation from \(T\) to \(U\).

Answer:

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