Question

figure b is the result of a transformation on figure a. which transformation would accomplish this?
answer
a rotation 90° clockwise about the origin
a rotation 180° counterclockwise about the origin
a translation 4 units to the left and 4 units up
a reflection over the y - axis

Explanation:

Step1: Analyze translation

Translation moves the figure without rotation. But Figure B is not just a shifted version of Figure A (as it has a rotational aspect).

Step2: Analyze reflection

Reflection over the \(y -\)axis would flip the figure horizontally. But Figure B is not a simple \(y -\)axis reflection of Figure A (as there is a vertical shift involved).

Step3: Analyze rotation \(90^{\circ}\) clockwise

A \(90^{\circ}\) clockwise rotation about the origin changes the coordinates \((x,y)\) to \((y, - x)\). This does not match the transformation from Figure A to Figure B.

Step4: Analyze translation \(4\) units left and \(4\) units up

If we take a point \((x,y)\) in Figure A and apply the translation \((x - 4,y + 4)\). For example, if a point in Figure A is \((2,-2)\), after translation \(x=2-4=-2\) and \(y=-2 + 4=2\). This matches the general position change from Figure A to Figure B.

Answer:

A translation 4 units to the left and 4 units up