Unit 2, Lesson 2
Circular Grid
Grade 8
2.1
Warm-up
What do you notice? What do you wonder?
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What do you notice? What do you wonder?
Here are two circles drawn on a circular grid with point at the center.
Here is a polygon .
Quadrilateral E F G H, center point Q and ray Q E on a circular grid. Point H is to the lower left on circle 3, point E is the upper left on circle 3, point F is the upper right on circle 6 and point G is lower right on circle 9. Point A is on circle 1 on ray Q E.
Dilate polygon using as the center of dilation and a scale factor of . , the image of , is already shown on the diagram. (You may need to use a straightedge to draw more rays from in order to find the images of other points.)
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 this diagram, is the center of dilation and the scale factor is 2.
Each point of triangle stays on the same ray from , but its distance from doubles.
Since the circles on a circular grid are the same distance apart, we can simply count units from the center to a given point and use the scale factor to determine where the new point should be located, making the circular grid useful for performing dilations.
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 .