Geometric Transformations and Reflections

Mr. Walker introduces the concept of transformations, focusing on reflections. He explains how reflections map points across a line to create mirror images. The lesson covers graphing lines on the coordinate plane, including the x-axis, y-axis, and lines like y=x and y=-x. Mr. Walker provides examples and practice problems to help students understand how to perform reflections over various lines, emphasizing the importance of maintaining equal distances from the line of reflection.

What is a transformation in geometry?

• A function that changes the size of a figure

• A function that changes the color of a figure

• A function that rotates a figure

• A function that maps a figure onto a new figure

What is the main characteristic of a translation?

• It changes the size of the shape

• It reflects the shape

• It moves the shape to a new position without changing its orientation

• It rotates the shape

Which axis is highlighted in blue and is horizontal on the coordinate plane?

• x-axis

• y-axis

• z-axis

• w-axis

What is the equation of the line that goes from the bottom left to the top right of the coordinate plane?

• x = -y

• y = -x

• y = x

• x = y

What happens to the y-coordinate of a point when it is reflected over the x-axis?

• It doubles

• It becomes zero

• It remains the same

• It changes to its opposite sign

When reflecting over the line y = x, what transformation occurs to the coordinates of a point?

• The y coordinate is doubled

• The x coordinate is doubled

• The x and y coordinates are swapped

• The x and y coordinates remain the same

In a reflection over y = -x, what happens to the coordinates of a point?

• The x and y coordinates are swapped and their signs are changed

• The x coordinate is doubled

• The y coordinate is doubled

• The x and y coordinates remain the same

If a point is on the line of reflection, what happens to it after the reflection?

• It disappears

• It doubles in distance from the line

• It remains on the line of reflection

• It moves to a new position

What is the new coordinate of the point (3, 4) after reflecting over the x-axis?

• (-3, -4)

• (3, 4)

• (3, -4)

• (-3, 4)

Which reflection line changes both the x and y coordinates to their opposite signs?

• x = -y

• y = -x

• x = y

• y = x