Question

1. perform the following sequence of transformations on the quadrilateral abcd. rotate 90° counterclockwise around the point (-3, -2), then translate up 1 and left 3 and label.

Explanation:

Step1: Recall rotation formula

Let $(x,y)$ be a point and $(a,b)$ be the center of rotation. The formula for a 90 - degree counter - clockwise rotation around the point $(a,b)$ is $(x',y')=(a-(y - b),b+(x - a))$.

Step2: Identify vertices of ABCD

Assume the vertices of the quadrilateral ABCD are $(x_1,y_1),(x_2,y_2),(x_3,y_3),(x_4,y_4)$. For each vertex, apply the rotation formula with $a=-3$ and $b = - 2$. For example, if a vertex is $(x,y)$, the rotated vertex $(x_{r},y_{r})$ is $x_{r}=-3-(y + 2)$ and $y_{r}=-2+(x + 3)$.

Step3: Apply translation

After rotation, to translate a point $(x_{r},y_{r})$ up 1 and left 3, use the translation rule $(x_{t},y_{t})=(x_{r}-3,y_{r}+1)$.

Answer:

The new vertices of the transformed quadrilateral are obtained by first rotating each vertex of ABCD 90 - degree counter - clockwise around the point $(-3,-2)$ using the rotation formula and then translating the rotated vertices up 1 and left 3 using the translation rule. The specific coordinates depend on the original coordinates of the vertices of quadrilateral ABCD.