Extra Credit Part 1 of Lesson 7 Constructing Rotations

Which of the following constructions were mentioned as being covered prior to constructing rotations?

• Parallel line constructions, perpendicular line constructions, and angle bisector constructions.

• Circle constructions, tangent line constructions, and segment bisector constructions.

• Triangle constructions, square constructions, and hexagon constructions.

• Arc constructions, ray constructions, and plane constructions.

When performing a 180° rotation of point A about point C to get A', what geometric relationship must exist between A, C, and A'?

• A, C, and A' must form an isosceles triangle.

• A, C, and A' must be collinear.

• A, C, and A' must form a right angle.

• A, C, and A' must be equidistant from each other.

What is another name for a 180° rotation about a point?

• Line reflection

• Translation

• Point reflection

• Glide reflection

What type of line construction is utilized to rotate points by 90 degrees?

• Parallel line construction

• Perpendicular line construction

• Angle bisector construction

• Segment bisector construction

When constructing a line perpendicular to a given line segment through a point on the segment, what is the initial step using a compass?

• Draw an arc centered at one endpoint of the segment.

• Draw an arc centered at the given point, intersecting the segment on both sides.

• Measure the distance from the given point to an arbitrary point.

• Draw a straight line through the given point.

In a 90-degree rotation about a point, what is the primary role of constructing a line perpendicular to the line connecting the pre-image and the center of rotation, passing through the center of rotation?

• To determine the exact length of the radius of rotation.

• To create a reference line that forms the required 90-degree angle for the rotation.

• To bisect the original line segment that connects the pre-image and the center.

• To establish a parallel line for translation before rotation.

To locate the image point A' after rotating point A by 90 degrees counterclockwise about point C, given a perpendicular line through C, what is the next step?

• Draw an arc centered at A with a radius equal to the distance from A to the perpendicular line.

• Draw a line from A to the perpendicular line.

• Draw an arc centered at C with radius CA, intersecting the perpendicular line.

• Measure the angle between AC and the perpendicular line.

What is the general strategy for rotating a line segment KL around a point M by a given angle?

• Draw a circle with center M and radius equal to the length of KL.

• Rotate point K to K', then rotate point L to L', and connect K'L'.

• Construct the perpendicular bisector of the segment KL.

• Measure the angle between the segment KL and the line connecting M to K.

When constructing a 90-degree rotation of point K around point M, after drawing the line segment KM, what is the next step to create the perpendicular line?

• Draw an arc centered at K.

• Place the compass point at M and draw arcs intersecting the line segment KM on both sides of M.

• Measure the length of KM.

• Draw a line parallel to KM.

What is the fundamental construction technique crucial for performing 90-degree rotations?

• Angle bisection.

• Constructing a perpendicular line through a point on a line.

• Copying a line segment.

• Constructing a parallel line.