Transformations and Reflections in Geometry

The video tutorial covers various geometric transformations, including reflections, translations, and rotations. It explains how to reflect figures across lines, translate figures using vectors, and rotate figures around a point. The tutorial also includes exercises on identifying lines of reflection, mapping points, and calculating angles of rotation. The video concludes with complex transformations like glide reflections and emphasizes labeling and connecting points accurately.

What is the first step in reflecting a figure across the line x = -1?

• Count the distance to the y-axis

• Mark the line x = -1

• Label the points

• Draw the figure

When reflecting across the y-axis, what should you do after counting to the y-axis?

• Erase the original figure

• Continue beyond the y-axis

• Draw a new figure

• Label the original points

How do you determine the line of reflection for a diagonal reflection?

• Use the x-axis

• Use the y-axis

• Use the equation y = something

• Use the equation y = x

What is the line of reflection when reflecting over y = 3?

• x = -3

• x = 3

• y = 3

• y = -3

In a translation along the vector (4, -5), what does the number 4 indicate?

• Move left 4

• Move up 4

• Move right 4

• Move down 4

What is the first step in graphing a figure with given vertices?

• Translate the figure

• Label the points

• Plot the points

• Draw the figure

How do you find the vector associated with a translation from C to A?

• Count the distance left and up

• Count the distance right and down

• Use the distance formula

• Use the midpoint formula

To find the translation vector, what operation is performed between u' and u?

• Division

• Multiplication

• Subtraction

• Addition

What is the combined translation of (4, -3) and (-2, 4)?

• (0, 0)

• (1, 1)

• (1, 2)

• (2, 1)

What is the result of rotating a point 90 degrees about the origin?

• Change sign of x and y

• Keep x and y the same

• Swap x and y, change sign of y

• Swap x and y, change sign of x