EFG is rotated -90° clockwise to create XYZ which of the following statements must be true
If EFG is rotated -90° clockwise to create XYZ, the following statements must be true:
1. The side EF coincides with the side XY.
2. The side FG coincides with the side YZ.
3. The side GE coincides with the side ZX.
In other words, the corresponding sides of EFG and XYZ would line up after the rotation.
1. The length of EY is equal to the length of XF.
2. The angle EYX is equal to the angle EXF.
3. The distance between the points E and X is equal to the distance between the points F and Y.
4. The angle between the lines EY and XF is 90°.
5. The segment EY is perpendicular to the line XF.
6. The angle EYF is equal to the angle FXY.
7. The length of YX is equal to the length of EG.
8. The point G lies on the line XY.
To determine which of the following statements must be true when EFG is rotated -90° clockwise to create XYZ, we should analyze the effect of a -90° clockwise rotation on the shape.
A -90° clockwise rotation means that each point of the original shape is rotated 90 degrees in the clockwise direction around a fixed point. In this case, the fixed point is the center of rotation.
Now, let's consider the possible statements:
1. The size of XYZ is smaller or equal to EFG.
2. The shape of XYZ is congruent to EFG.
3. XYZ has the same orientation as EFG.
4. XYZ has the same perimeter as EFG.
To determine which statements must be true, we need to analyze the effects of a -90° clockwise rotation on the shape:
1. The size of XYZ is smaller or equal to EFG:
This statement may or may not be true. The size of XYZ could be smaller or equal to EFG if the rotation causes certain points to move closer to the center of rotation. However, this is not always the case. If some points move away from the center of rotation, XYZ could end up larger than EFG.
2. The shape of XYZ is congruent to EFG:
This statement is true. A -90° clockwise rotation does not change the shape of the original figure. It only changes the position of the points.
3. XYZ has the same orientation as EFG:
This statement is false. A -90° clockwise rotation changes the orientation of the shape. The orientation of XYZ is different from EFG because the direction of the rotation is clockwise.
4. XYZ has the same perimeter as EFG:
This statement is false. A -90° clockwise rotation can change the position of the points, which affects the perimeter of the shape.
Therefore, the only statement that must be true when EFG is rotated -90° clockwise to create XYZ is: "The shape of XYZ is congruent to EFG."