Geo L2.4 Reflection

Lesson 2.4 Reflection

Geometry

Vocabulary

• Rigid Transformation: does not change the side lengths or angle measures of a figure

• Reflection: a rigid transformation moves each pre-image point across a line such that the line is the perpendicular bisector of the segment connecting each pre-image point with its image 

• Perpendicular Bisector: a line or segment that passes through the midpoint of a segment at a 90° angle.

Line of Reflection

• A point in the image and its corresponding point in the pre-image are equidistant from the line of reflection

• All the lines connecting points in

  the image with points in the

  pre-image are perpendicular to

  the line of reflection

Open Ended

According to the definition, is this a reflection? Explain.

Orientation

• Clockwise (CW) vs. Counterclockwise (CCW)

• What happens to the orientation of the pre-image points when they are reflected?

Open Ended

What is the equation of the line of reflection?

Multiple Choice

When you reflect a figure across the y-axis, the vertical height of each point is unchanged, but the horizontal value of the image is the opposite of the pre-image. (x, y)→

• (-x, y)

• (x, -y)

• (y, -x)

Multiple Choice

Reflect A(3, -8) across the y-axis.

• A'(3, 8)

• A'(-3, 8)

• A'(-3, -8)

Multiple Choice

When you reflect a figure across the x-axis, the horizontal position of each point is unchanged, but the vertical value of the image is the opposite of the pre-image. (x, y)→

• (-x, y)

• (x, -y)

• (y, -x)

Multiple Choice

Reflect A(3, -8) across the x-axis.

• A'(3, 8)

• A'(-3, 8)

• A'(-3, -8)

Multiple Choice

When you reflect a figure across the line y=x, the horizontal and vertical position of each point interchange. (x, y)→

• (-x, y)

• (y, x)

• (y, -x)

Multiple Choice

Reflect A(3, -8) across the line y=x

• A'(8, 3)

• A'(-3, 8)

• A'(-8, 3)

Multiple Choice

Is this a reflection?

• Yes

• No

Multiple Choice

Is this a reflection?

• Yes

• No

Open Ended

Reflect the point (7, -2) across the x-axis and tell the coordinates of the image.

Open Ended

Reflect the point (7, -2) across the y-axis and tell the coordinates of the image.

Open Ended

Reflect the point (7, -2) across the line y=x and tell the coordinates of the image.