Question

question
figure l is the result of a transformation on figure k. which transformation would accomplish this?
answer
a translation 1 unit to the right and 5 units down
a rotation 180° counterclockwise about the origin
a rotation 90° counterclockwise about the origin
a rotation 90° clockwise about the origin

Explanation:

Step1: Recall rotation rules

• For a \(90^{\circ}\) clockwise rotation about the origin \((x,y)\to(y, -x)\)
• For a \(90^{\circ}\) counter - clockwise rotation about the origin \((x,y)\to(-y,x)\)
• For a \(180^{\circ}\) rotation about the origin \((x,y)\to(-x,-y)\)
• For a translation \((x,y)\to(x + a,y + b)\)

Step2: Analyze the transformation

Let's assume a point on Figure \(K\). Suppose a vertex of Figure \(K\) is \((-1,-2)\). After a \(180^{\circ}\) counter - clockwise (or clockwise, since \(180^{\circ}\) rotation is same for both directions) rotation about the origin \((x,y)\to(-x,-y)\). So \((-1,-2)\to(1,2)\) which is a vertex of Figure \(L\).

Answer:

A rotation \(180^{\circ}\) counterclockwise about the origin.