Question

1. quadrilateral math and its image math are graphed on the set of axes below. describe a sequence of transformations that maps quadrilateral math onto quadrilateral math.

Explanation:

Step1: Determine the rotation

First, observe the orientation change. Quadrilateral \(MATH\) to \(M''A''T''H''\) has a rotation. Rotating quadrilateral \(MATH\) \(180^{\circ}\) about the origin changes the sign of both \(x\) and \(y\) coordinates of its vertices. For a point \((x,y)\) on \(MATH\), after a \(180^{\circ}\) rotation about the origin, it becomes \((-x, -y)\).

Step2: Determine the translation

After the \(180^{\circ}\) rotation, we need to check for translation. Let's assume a general vertex - based approach. If we consider the center - like behavior (since it's a rigid transformation combination). After the \(180^{\circ}\) rotation, we then translate the rotated figure. A translation of \(1\) unit to the left (subtracting \(1\) from the \(x\) - coordinate) and \(1\) unit up (adding \(1\) to the \(y\) - coordinate) of the \(180^{\circ}\) - rotated quadrilateral \(MATH\) (about the origin) maps it to \(M''A''T''H''\).

Answer:

Rotate quadrilateral \(MATH\) \(180^{\circ}\) about the origin and then translate it \(1\) unit to the left and \(1\) unit up.