Question

c. here are some points: what are the coordinates of g, h, and i after a rotation about (0,0) by 90°. plot these points on the grid, and label them g, h and i. from unit 1, lesson 4 describe a sequence of transformations that takes trapezoid a to trapezoid b.

Explanation:

Step1: Recall rotation rules

For a 90 - degree counter - clockwise rotation about the origin $(0,0)$, the transformation rule for a point $(x,y)$ is $(x,y)\to(-y,x)$.

Step2: Find coordinates of $G$

If $G=(-1,3)$, then $G'=(-3, - 1)$ using the rotation rule $(x,y)\to(-y,x)$.

Step3: Find coordinates of $H$

If $H = (-4,0)$, then $H'=(0,-4)$ using the rotation rule $(x,y)\to(-y,x)$.

Step4: Find coordinates of $I$

If $I=(3,-2)$, then $I'=(2,3)$ using the rotation rule $(x,y)\to(-y,x)$.

Step5: Describe trapezoid transformation

To describe the transformation from trapezoid A to trapezoid B, first, we need to analyze the orientation, position and size changes. Assume trapezoid A has vertices $(x_1,y_1),(x_2,y_2),(x_3,y_3),(x_4,y_4)$ and trapezoid B has vertices $(x_1',y_1'),(x_2',y_2'),(x_3',y_3'),(x_4',y_4')$. We may need to consider translation (shifting), rotation (turning) and reflection (flipping). A possible sequence could be a rotation about a certain point (e.g., the origin) followed by a translation. For example, if the rotation makes the trapezoid have the right orientation and then a translation moves it to the correct position.

Answer:

Coordinates of $G'$: $(-3,-1)$
Coordinates of $H'$: $(0, - 4)$
Coordinates of $I'$: $(2,3)$
A possible sequence of transformations from trapezoid A to trapezoid B: A 90 - degree counter - clockwise rotation about a point (possibly the origin) followed by a translation.