Question

ximena draws an x - shape in the coordinate plane as shown. draw the images of ximenas x - shape rotated 90° counterclockwise, 180° clockwise, and 270° counterclockwise around the origin. label each image with the degree of rotation and direction.

Explanation:

Step1: Recall rotation rules

For a 90 - degree counter - clockwise rotation about the origin, the transformation rule for a point $(x,y)$ is $(-y,x)$. For a 180 - degree clockwise rotation (same as 180 - degree counter - clockwise rotation), the rule is $(-x,-y)$. For a 270 - degree counter - clockwise rotation (same as 90 - degree clockwise rotation), the rule is $(y, - x)$.

Step2: Rotate key points

Identify the key points of the X - shape. For each key point $(x,y)$ of the original X - shape, apply the above rotation rules to find the new coordinates. Then connect the new points to form the rotated shapes.

Step3: Label the images

Label each new image with the corresponding degree of rotation and direction (e.g., "90° counter - clockwise", "180° clockwise", "270° counter - clockwise").

This is a geometric transformation problem. To actually draw the images, one would need to use graph paper or a graphing tool. But the general steps for finding the rotated shapes are as described above. Since we can't draw in this text - based format, the steps for calculating the new coordinates of the key points of the shape are provided.

Answer:

Step1: Recall rotation rules

For a 90 - degree counter - clockwise rotation about the origin, the transformation rule for a point $(x,y)$ is $(-y,x)$. For a 180 - degree clockwise rotation (same as 180 - degree counter - clockwise rotation), the rule is $(-x,-y)$. For a 270 - degree counter - clockwise rotation (same as 90 - degree clockwise rotation), the rule is $(y, - x)$.

Step2: Rotate key points

Identify the key points of the X - shape. For each key point $(x,y)$ of the original X - shape, apply the above rotation rules to find the new coordinates. Then connect the new points to form the rotated shapes.

Step3: Label the images

Label each new image with the corresponding degree of rotation and direction (e.g., "90° counter - clockwise", "180° clockwise", "270° counter - clockwise").

This is a geometric transformation problem. To actually draw the images, one would need to use graph paper or a graphing tool. But the general steps for finding the rotated shapes are as described above. Since we can't draw in this text - based format, the steps for calculating the new coordinates of the key points of the shape are provided.