Dilation and Scale Factor Concepts

The video tutorial explains the concept of dilation on a coordinate plane using three examples. Example A demonstrates dilating a quadrilateral with a scale factor of 1.5, showing how to calculate new coordinates. Example B involves determining the coordinates and scale factor for two triangles, illustrating the multiplication needed to transform original points. Example C uses the distance formula to prove that dilation preserves the shape of figures, confirming that the sides of the dilated figure are proportional to the original.

What is the result of applying a scale factor of 1.5 to the coordinates of a point at (-4, -2)?

• (-8, -4)

• (-2, -1)

• (-6, -3)

• (-5, -2.5)

If a quadrilateral is dilated with a scale factor of 1.5, what happens to its shape?

• It becomes a different shape.

• It remains the same shape but changes size.

• It rotates 90 degrees.

• It reflects over the x-axis.

What are the coordinates of point A in the dilated triangle A'B'C' if A is at (2, 1) and the scale factor is 3?

• (6, 3)

• (5, 4)

• (3, 2)

• (9, 6)

How do you determine the scale factor between two similar triangles?

• By adding the coordinates of corresponding points.

• By subtracting the coordinates of the original triangle from the dilated.

• By dividing the coordinates of the dilated triangle by the original.

• By multiplying the coordinates of the original triangle by 2.

What is the scale factor if point C at (3, 6) is dilated to C' at (9, 18)?

• 5

• 4

• 3

• 2

Using the distance formula, what is the length of side AB in the original triangle if A is at (2, 1) and B is at (5, 1)?

• 2 units

• 3 units

• 4 units

• 5 units

What is the length of side A'B' in the dilated triangle if A' is at (6, 3) and B' is at (15, 3)?

• 6 units

• 7 units

• 8 units

• 9 units

How does the distance formula help in verifying that dilations preserve shape?

• By confirming that the area is doubled.

• By demonstrating that side lengths are proportional.

• By proving that the perimeter is unchanged.

• By showing that angles remain the same.

If the original side length is the square root of 26, what is the side length in the dilated triangle with a scale factor of 3?

• 4 times the square root of 26

• 3 times the square root of 26

• Square root of 26

• 2 times the square root of 26

What is the relationship between the side lengths of the original and dilated figures?

• The side lengths of the dilated figure are twice the original.

• The side lengths of the dilated figure are four times the original.

• The side lengths of the dilated figure are half of the original.

• The side lengths of the dilated figure are three times the original.