Question

figure b is the result of a transformation on figure a. which transformation would accomplish this? a. a translation 2 units to the right. b. a translation 2 units to the left. c. a reflection over the x -axis d. a reflection over the y -axis

Explanation:

Step1: Observe the position change

Compare the corresponding points of Figure A and Figure B. We can see that for each point \((x,y)\) in Figure A, the \(x -\)coordinate of the corresponding point in Figure B is \(x - 2\) and the \(y -\)coordinate remains the same.

Step2: Recall transformation rules

A translation of \(a\) units to the left for a point \((x,y)\) gives the new point \((x - a,y)\), and a translation of \(a\) units to the right gives \((x + a,y)\). A reflection over the \(x -\)axis changes the point \((x,y)\) to \((x,-y)\) and a reflection over the \(y -\)axis changes the point \((x,y)\) to \((-x,y)\).

Step3: Determine the transformation

Since the \(x -\)coordinates of points in Figure A are decreased by 2 to get the points in Figure B and \(y -\)coordinates remain the same, it is a translation 2 units to the left.

Answer:

B. A translation 2 units to the left.