Question

four triangles are shown on the coordinate grid. triangles wnk, tmh, and cxl are all rotations of △ rfb. 5. on the coordinate grid draw angle fdk. 6. describe how the measure of ∠fdk can be used to determine the degrees of rotation where △ rfb is the pre - image and △ nkw is the image. 7. describe how the coordinates of the vertices of △ rfb, the preimage, and the coordinates of △ nkw, the image can be used to determine the degrees of rotation. 8. describe the rotation where △ rfb is the preimage and △ cxl is the image. 9. describe how the coordinates of the vertices of △ rfb and △ tmh show that rotating △ rfb 180° about the origin results in △ mht. 10. explain why the rotation of △ rfb that results in △ mht can be described as 180° clockwise or 180° counterclockwise.

Explanation:

Step1: Understanding rotation concept

In a rotation of a geometric - figure about a point, the angle of rotation is the angle between a line segment connecting the center of rotation to a point on the pre - image and the corresponding line segment connecting the center of rotation to the corresponding point on the image.

Step2: For question 6

The measure of ∠FDK is the angle of rotation. When △RFB is rotated to △NKW, the center of rotation is point D. The angle between the line segment from D to a vertex of △RFB (e.g., DF) and the line segment from D to the corresponding vertex of △NKW (e.g., DK) is ∠FDK. So, the measure of ∠FDK gives the number of degrees of rotation.

Step3: For question 7

If the center of rotation is the origin (0,0), for a 90 - degree counter - clockwise rotation, the transformation rule for a point (x,y) is (-y,x). For a 180 - degree rotation, the rule is (-x,-y). By comparing the coordinates of the vertices of △RFB (x1,y1) and △NKW (x2,y2), we can determine the transformation rule and thus the angle of rotation. For example, if (x1,y1)→(-y1,x1), it's a 90 - degree counter - clockwise rotation; if (x1,y1)→(-x1,-y1), it's a 180 - degree rotation.

Step4: For question 8

As indicated, the rotation from △RFB to △CXL is a 90 - degree counter - clockwise rotation. When rotating a point (x,y) 90 degrees counter - clockwise about the origin, the new coordinates (x',y') are (-y,x). We can check the coordinates of the vertices of △RFB and △CXL to confirm this transformation.

Step5: For question 9

For a 180 - degree rotation about the origin, the transformation rule for a point (x,y) is (-x,-y). If we take the coordinates of the vertices of △RFB and apply the (-x,-y) rule, we will get the coordinates of the vertices of △MHT. For example, if a vertex of △RFB is (a,b), after a 180 - degree rotation about the origin, its corresponding vertex in △MHT will be (-a,-b).

Step6: For question 10

A 180 - degree clockwise rotation and a 180 - degree counter - clockwise rotation result in the same transformation. The transformation rule for both is (x,y)→(-x,-y). So, whether we rotate △RFB 180 degrees clockwise or 180 degrees counter - clockwise about the origin, we will get △MHT because the end - result of swapping the signs of both x and y coordinates is the same regardless of the direction (clockwise or counter - clockwise) for a 180 - degree rotation.

Answer:

1. The measure of ∠FDK is the angle of rotation from △RFB to △NKW as it is the angle between the lines connecting the center of rotation D to corresponding vertices of the pre - image and image.
2. By comparing the coordinates of vertices of △RFB and △NKW and applying rotation transformation rules (e.g., (x,y)→(-y,x) for 90 - degree counter - clockwise, (x,y)→(-x,-y) for 180 - degree rotation) about the origin, we can determine the angle of rotation.
3. It is a 90 - degree counter - clockwise rotation as per the indicated answer, and this can be verified by the 90 - degree counter - clockwise rotation transformation rule (x,y)→(-y,x) for vertices.
4. Applying the 180 - degree rotation rule (x,y)→(-x,-y) about the origin to the vertices of △RFB gives the vertices of △MHT.
5. A 180 - degree clockwise and a 180 - degree counter - clockwise rotation about the origin have the same transformation rule (x,y)→(-x,-y), so the rotation of △RFB to △MHT can be described as either 180 degrees clockwise or 180 degrees counter - clockwise.

(Note: For question 5, since it requires drawing on a coordinate grid, it's not possible to provide a drawn - out answer in this text - based format, but the process would be to locate points F, D, and K on the given grid and draw the angle.)