Dilation of Triangles Concepts

The video tutorial explains the concept of geometric dilation using a triangle ABC. The teacher demonstrates how to graph the dilation of the triangle with a scale factor of two, resulting in a larger, similar triangle. The process involves multiplying each coordinate by the scale factor and plotting the new points. The tutorial further explores the similarity between the original and dilated triangles by comparing their side lengths and calculating distances using the distance formula. The video concludes by confirming the proportionality and similarity of the triangles through side-side-side similarity, emphasizing the consistent ratios of corresponding sides.

What is the initial step in graphing the dilation of a triangle with a scale factor of two?

• Plotting the original triangle

• Calculating the new coordinates

• Drawing the new triangle

• Measuring the side lengths

How do you determine the new coordinates of a point after dilation?

• Multiply each coordinate by the scale factor

• Subtract the scale factor from each coordinate

• Divide each coordinate by the scale factor

• Add the scale factor to each coordinate

What is the new coordinate of point A (0, 3) after dilation by a scale factor of two?

• (6, 0)

• (0, 3)

• (3, 0)

• (0, 6)

Which formula is used to calculate the distance between two points in a plane?

• Volume formula

• Distance formula

• Slope formula

• Area formula

What is the distance between points A (0, 3) and B (2, 4) in the original triangle?

• 10

• 5

• Square root of 5

• Square root of 34

What is the ratio of the side lengths of the dilated triangle to the original triangle?

• 1:1

• 4:1

• 2:1

• 3:1

Which similarity criterion is used to verify the similarity of the original and dilated triangles?

• Angle-Side-Angle

• Side-Side-Side

• Side-Angle-Side

• Angle-Angle-Angle

What happens to a geometric figure when it is dilated by a non-zero scale factor?

• It remains the same size

• It becomes a different shape

• It becomes similar to the original

• It disappears

What is the significance of the scale factor in dilation?

• It has no effect on the figure

• It changes the size of the figure

• It affects the orientation of the figure

• It determines the color of the figure

What is the result of dilating a triangle by a scale factor of zero?

• A larger triangle

• A similar triangle

• A point

• An identical triangle