Question

problem 3 describe a sequence of transformations that moves the shaded figure onto the unshaded figure. rotate the shaded figure 90 degrees clockwise, then translate it left

Explanation:

Step1: Analyze Rotation

First, we rotate the shaded figure 90 degrees clockwise. A 90 - degree clockwise rotation of a point \((x,y)\) around the origin (or a suitable center) follows the rule \((x,y)\to(y, - x)\). For the given figure, we identify the key vertices of the shaded figure and apply this rotation rule.

Step2: Analyze Translation

After the rotation, we need to translate the rotated figure to the left. Translating a figure to the left means subtracting a certain number of units from the \(x\) - coordinate of each vertex of the rotated figure. By observing the positions of the shaded and unshaded figures, we determine the appropriate number of units to translate left so that the rotated and translated figure coincides with the unshaded figure.

Answer:

To move the shaded figure onto the unshaded figure, first rotate the shaded figure 90 degrees clockwise about an appropriate center (e.g., a common vertex or the origin - like point in the grid), then translate the rotated figure a certain number of units to the left (the number of units can be determined by comparing the horizontal positions of corresponding vertices of the rotated shaded figure and the unshaded figure). The sequence is: Rotate the shaded figure 90 degrees clockwise, then translate it left.