Geometry Reflection

Students will be able to reflect an object or point across an axis or line.

​

​Learning Target

Draw

Place the numbers 1 to 5 in the circles above, one number per circle, so that the sum of numbers on each of the two diagonal lines is 9.

​Solution

1

2

​3

4

​5

​Translation from Yesterday's Lesson

Multiple Choice

Select the picture showing a translation of:

2 squares right and 1 square up

Multiple Choice

Select the picture which shows a translation:

4 squares right and 5 squares down

Multiple Choice

Which picture shows a TRANSLATION?

Multiple Choice

What transformation is happening?
(x, y) ----> (x + 2, y - 3) 

• slide up 2, left 3
• slide right 2, up 3
• slide right 2, down 3
• slide left 3, right 2

Multiple Choice

Which rule correctly describes this translation?

• (x - 6, y + 2)

• (x - 2, y + 6)

• (x + 2, y - 6)

• (x + 6, y - 2)

​Reflection Across the y-axis, x-axis and a Line

Note, the new new object is equal distance from the reflection axis or line of reflection.

Using your board, graph paper or Desmos,
create the pre-image and the reflected image.

​Did your image look like this?

​Reflect the image across the x and y axis

​Use your board or Desmos to project the images.

In Desmos, Label the points, and use the polygon function to show the images. Your new image show be label P', Q' and R'.

​Reflection Across a Line

​Reflection across the line y = x: (x, y) -> (y, x)

Reflection across the line y = -x: (x, y) -> (-y, x)

Multiple Choice

What is the Algebraic Notation for this Reflection?

• (x, y) → (y, x)

• (x, y) → (-x, y)

• (x, y) → (-y, -x)

• (x, y) → (x, -y)

Draw

Reflect QRST across the x-axis

Draw

Name the coordinates of your reflection. Use your board

Use your board or Desmos to project the images.

In Desmos, Label the points, and use the polygon function to show the images. Your new image show be label P', Q' and R'.

Multiple Choice

Which of the following represents a single reflection of Figure 1?

• A

• B

• C

• D

Multiple Choice

Describe the transformation shown in the graph.

• Reflect over x-axis
• Reflect over y-axis
• Rotate 180 degrees
• Translate 4 units right

Multiple Choice

Describe the transformation shown on the graph.

• Reflect over x-axis
• Reflect over y-axis
• Rotate 180 degrees
• Rotate 90 degrees CCW

Multiple Choice

Find K' if the figure is reflected across the x-axis

• (4, 1))
• (-1, -4)
• (1, -4)
• (1, 4)

Multiple Choice

State the line of reflection.

• Reflection across y-axis
• Reflection across x-axis
• Reflection across x = 1
• Reflection across y = 1

Multiple Choice

Describe the point (3, -7) -> (-3, -7)

• Reflection across the

  x-axis

• Reflection across the

  y-axis

• Reflection across the

  z-axis

• no reflection