Dilation from a Point: Key Concepts and Applications

The video tutorial explains the concept of dilation in geometry, starting with a simple case where the center is at the origin. It then progresses to more complex scenarios where the center is not at the origin, using specific examples to illustrate the process. The tutorial covers how to calculate new points after dilation with different centers and scale factors, including a case where the scale factor is less than one, demonstrating how the image shrinks. The video encourages viewers to practice with additional problems to reinforce understanding.

What is the result of a dilation with a scale factor of 2 when the center is at (0,0)?

• The shape becomes twice its original size.

• The shape remains the same size.

• The shape becomes four times its original size.

• The shape becomes half its original size.

If the center of dilation is at (-3, 5) and point A is at (-3, -1), how many units down should the new point A' be if the scale factor is 2?

• 6 units

• 9 units

• 12 units

• 3 units

For a dilation with center at (-3, 5) and point B at (-1, 2), what are the coordinates of B' if the scale factor is 2?

• (1, -1)

• (2, 4)

• (0, 0)

• (1, 1)

When dilating point C at (1, -2) with a center at (-3, 5) and a scale factor of 2, what are the coordinates of C'?

• (5, -9)

• (4, -8)

• (6, -10)

• (3, -7)

In the second example, if the center is at (-4, -2) and point A is at (-3, -1), what are the coordinates of A' with a scale factor of 2?

• (-1, 1)

• (-3, -1)

• (-2, 0)

• (-4, -2)

For the second example, if point B is at (-1, 2) and the center is at (-4, -2), what are the coordinates of B' with a scale factor of 2?

• (2, 6)

• (1, 5)

• (0, 4)

• (3, 7)

In the second example, if point C is at (1, -2) and the center is at (-4, -2), what are the coordinates of C' with a scale factor of 2?

• (3, -4)

• (4, -3)

• (5, -1)

• (6, -2)

When the scale factor is 1/2 and the center is at (4, -3), what are the coordinates of A' if point A is at (-10, 3)?

• (-3, 0)

• (-2, 1)

• (-4, 2)

• (-5, 3)

For a scale factor of 1/2 and center at (4, -3), what are the coordinates of B' if point B is at (-6, 9)?

• (-1, 3)

• (-2, 4)

• (-3, 5)

• (-4, 6)

In the example with a scale factor of 1/2, what are the coordinates of C' if point C is at (-2, 1) and the center is at (4, -3)?

• (3, 1)

• (1, -1)

• (2, 0)

• (4, 2)