Unit 2, Lesson 9
Dilations
Accelerated 7
9.1
Warm-up
What do you notice? What do you wonder?
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What do you notice? What do you wonder?
Here is a polygon .
Here is a diagram that shows 9 points.
Nine points. Points E, F, G and H are mostly horizontal, spread out evenly and form a line. Point A above F, and point B above G, point H and Point I below and to the right also form a line. Point F, point D, point B and point C far above between point G and H also form a line.
Draw the images of points and using as the center of dilation and a scale factor of . Label the new points and .
Pause here so your teacher can review your diagram. Your teacher will then give you a scale factor to use in the next part.
Let's make a perspective drawing. Here is a rectangle.
Choose a point inside the shaded circular region but outside the rectangle to use as the center of dilation. Label it .
Use your center and the scale factor you were given to draw the image under the dilation of each vertex of the rectangle, one at a time. Connect the dilated vertices to create the dilated rectangle.
Draw segments that connects each of the original vertices with its image. This will make your diagram look like a cool three-dimensional drawing of a box! If time allows, you can shade the sides of the box to make it look more realistic.
Compare your drawing to other people’s drawings. What is the same and what is different? How do the choices you made affect the final drawing? Was your dilated rectangle closer to than to the original rectangle, or farther away? How is that decided?
A dilation is a transformation in which each point on a figure moves along a line and changes its distance from a fixed point, called the center of dilation. All of the original distances are multiplied by the same scale factor.
In the figure, point is dilated with the center of dilation at .
Since point is farther away from than , the scale factor is larger than 1. If we measure the distance between and , we would find that it is exactly twice the distance between and , meaning the scale factor of the dilation is 2.
Since point is closer to than , the scale factor is smaller than 1. If we measure the distance between and , we would find that it is one third the distance between and , meaning the scale factor of the dilation is .
A dilation is a transformation that can reduce or enlarge a figure. Each point on the figure moves along a line closer to or farther from a fixed point. That fixed point is the center of the dilation. All of the original distances are multiplied by the same scale factor.
Triangle is a dilation of triangle . The center of dilation is . The scale factor is 3.
Every point of triangle is 3 times as far from as every corresponding point of triangle .