Question

determine a series of transformations that would map figure d onto figure e.
answer attempt 1 out of 2
a followed by a

Explanation:

Step1: Reflect Figure D over the y - axis

Reflecting a point \((x,y)\) over the \(y\) - axis gives the point \((-x,y)\). This will change the sign of the \(x\) - coordinates of all the vertices of Figure D.

Step2: Translate the reflected figure

Count the number of units needed to move the reflected figure to the position of Figure E. Observing the \(x\) and \(y\) coordinates of corresponding vertices, we find that after reflection over the \(y\) - axis, we need to translate the figure. For example, if a vertex of Figure D is \((-a,b)\) after reflection over the \(y\) - axis, and the corresponding vertex of Figure E is \((c,d)\), we calculate the horizontal and vertical shifts. The horizontal shift \(h=c - a\) (after reflection \(a\) is positive) and the vertical shift \(k=d - b\). In this case, after reflection over the \(y\) - axis, we translate the figure \(8\) units to the right (since \(-(- 8)+0 = 8\) for the \(x\) - coordinate adjustment of a vertex that was at \(x=-8\) in Figure D) and \(0\) units up (or down).

Answer:

Reflect over the \(y\) - axis followed by a translation \(8\) units to the right.