Question

in figure r? a. a translation of 7 units to the right b. a rotation of 90° clockwise about the origin c. a rotation of 270° counterclockwise about the origin d. a reflection over the y-axis followed by a translation of 1 unit to the right

Explanation:

To determine the transformation to get Figure R (assuming we analyze typical coordinate transformations):

• Option A: A 7 - unit right translation would shift all points 7 units right, but this is a simple translation and often not matching complex figure transformations.
• Option B: A \(90^{\circ}\) clockwise rotation about the origin has a transformation rule \((x,y)\to(y, - x)\).
• Option C: A \(270^{\circ}\) counter - clockwise rotation about the origin is equivalent to a \(90^{\circ}\) clockwise rotation (since \(360 - 270=90\)), same as option B's rule, which is not likely the correct unique transformation.
• Option D: A reflection over the \(y\) - axis transforms \((x,y)\to(-x,y)\), then a translation of 1 unit to the right transforms \((-x,y)\to(-x + 1,y)\). This two - step transformation is more likely to match the figure's transformation (assuming the figure has symmetry and shift characteristics that fit this).

Answer:

D. a reflection over the \(y\) - axis followed by a translation of 1 unit to the right