Dilations: scale factor and classification

Learning Objectives Define dilation, scale factor, and center of dilation. Identify the pre-image and image in a dilation. Apply a given scale factor to dilate a figure centered at the origin on a coordinate plane. Calculate the scale factor of a dilation given the pre-image and image. Classify a dilation as an enlargement or a reduction based on its scale factor. Describe the relationship between the pre-image and image in a dilation using geometric terms. Have you ever seen a picture on your phone and 'pinched' it to make it bigger or smaller? 🤏 That's a real-world example of a mathematical transformation called a dilation! In this lesson, you'll learn about dilations, a type of transformation that changes the size of a figure but not its shape. We&#0...

TermDefinitionExample DilationA transformation that changes the size of a figure by a specific scale factor, but preserves its shape and orientation. The new figure is similar to the original.If you have a small square and you make it twice as big, you've performed a dilation. Scale Factor (k)The ratio of a length in the image to the corresponding length in the pre-image. It determines how much the figure is enlarged or reduced.If a line segment of length 3 becomes a segment of length 6 after dilation, the scale factor is $k = 6/3 = 2$. Center of DilationA fixed point in the plane from which all points of a figure are 'stretched' or 'shrunk' during a dilation. It's the only point that doesn't move.When dilating a figure on a coordinate plane, the origin...

Dilation Rule (Centered at the Origin) $(x, y) \rightarrow (kx, ky)$ To dilate a point $(x, y)$ on a coordinate plane with the center of dilation at the origin $(0,0)$ and a scale factor $k$, multiply both the x-coordinate and the y-coordinate by $k$ to find the new coordinates of the image point. Calculating Scale Factor $k = \frac{\text{Length of Image Segment}}{\text{Length of Pre-image Segment}}$ To find the scale factor $k$ of a dilation, divide the length of any segment in the image by the length of its corresponding segment in the pre-image. The scale factor is always positive for Grade 8. Classifying Dilations If $k > 1$, the dilation is an enlargement. If $0 < k < 1$, the dilation is a reduction. If $k = 1$, the figure remains congruent (no change in...