Dilate triangle using center and a scale factor of 3.
3.2
Activity
All the Scale Factors
Here is a center of dilation and a triangle.
Measure the sides of triangle (to the nearest mm).
Your teacher will assign you a scale factor. Predict the relative lengths of the original figure and the image after you dilate by your scale factor.
Dilate triangle using center and your scale factor.
How does your prediction compare to the image you drew?
Use tracing paper to copy point , triangle , and your dilation. Label your tracing paper with your scale factor.
Align your tracing paper with your partner’s. What do you notice?
3.3
Activity
What Stays the Same?
Dilate quadrilateral using center and your scale factor.
Complete the table.
Ratio
Value
What do you notice? Can you prove your conjecture?
Complete the table.
Ratio
Value
What do you notice? Does the same reasoning you just used also prove this conjecture?
Student Lesson Summary
We know that a dilationwith center and positive scale factor,, takes a point along the ray to another point whose distance is times farther away from than is.
The triangle is a dilation of the triangle with center and with a scale factor of 2. So is 2 times farther away from than is, is 2 times farther away from than is, and is 2 times farther away from than is.
Because of the way dilations are defined, all of these quotients give the scale factor: .
If triangle is dilated from point with scale factor , then each vertex in is on the ray from P through the corresponding vertex of , and the distance from to each vertex in is one-third as far as the distance from to the corresponding vertex in .
The dilation of a line segment is longer or shorter according to the same ratio given by the scale factor. In other words, if segment is dilated from point with a scale factor of , then the length of segment is multiplied by to get the corresponding length of .
.
Corresponding side lengths of the original figure and dilated image are all in the same proportion, and are related by the same scale factor, .
Glossary
None
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