Question

in the diagram, figure g is congruent to figure g”.
what sequence of transformations can be performed
to show that the figures are congruent? show
your work.

Explanation:

Step1: Analyze the position and orientation

First, observe the position and orientation of the two figures. Figure \(G\) is in the fourth - quadrant and figure \(G''\) is in the second - quadrant.

Step2: Determine the rotation

Rotate figure \(G\) \(180^{\circ}\) about the origin. The rule for a \(180^{\circ}\) rotation about the origin \((x,y)\to(-x, - y)\).

Step3: Check the congruence

After a \(180^{\circ}\) rotation, the shape and size of the figure do not change. Since congruent figures have the same shape and size, a \(180^{\circ}\) rotation (a type of transformation) will show that the two figures are congruent.

Answer:

A \(180^{\circ}\) rotation about the origin.