Period: Date: Lesson 3B: Properties of Dilations and Equations of lines

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Name: Period: Date: : Properties of Dilations and Equations of lines Learning Targets I can identify the properties of dilation mentioned as followed: dilation takes a line not passing through the

1 Name: Period: Date: : Properties of Dilations and Equations of lines Learning Targets I can identify the properties of dilation mentioned as followed: dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. I can use properties of dilations to write equations of lines that have gone through dilation I can dilate points on the coordinate grid around with the center of dilation the origin Example 1. a. Dilate the segment AB that is part of a line whose equation is y = 2x + 5 about the center O(1,0) and scale factor of 2 b. What are the coordinates of points A and B c. Write the equation of A B (use Stats on calculator) d. What can we say about the equation of segments AB and A B e. What can you say about the y-intercepts? Explain

2 Name: Example 2. Period: Date: a. Dilate the segment AB that is part of a line whose equation is y = 2x + 5 about the center O(1,3) and scale factor of 2 b. What are the coordinates of points A and B c. Write the equation of A B (use Stats on calculator) d. What can we say about the equation of segments AB and A B e. What can you say about the y-intercepts? Explain Conclusion: Dilation with the scale factor of k takes a line with equation y = mx + b not passing through the center of dilation to another parallel line. Draw a picture The slope of the new line will The y-intercept will be Dilation with the scale factor of k leaves a line with equation y = mx + b passing through the center of dilation unchanged. Draw a picture The slope of the new line will The y-intercept will be

3 Name: Period: Date: Example 3 The equation of line h is 2x + y = 1. Line m is the image of line h after a dilation of scale factor 4 with respect to the origin. What is the equation of the line m? Thinking out loud (1) y = 2x + 1 Equation of Line m will be (2) y = 2x + 4 (3) y = 2x + 4 (4) y = 2x + 1 Is the center of dilation on the line? yes What is the slope of line m What is the y-intercept of line m -- no Example 4 Line is transformed by a dilation with a scale factor of 2 and centered at. The line's image is 1) 2) 3) 4) Example 5. The line image? is transformed by a dilation centered at the origin. Which linear equation could be its Thinking out loud Equation of line image will be Is the center of dilation on the line? yes -- no What is the slope of image line

4 Name: Period: Date: 6a. The line 4x + 2y = 4 is transformed by a dilation with the scale factor of 3 and centered at point (0, 0). Write the linear equation of its image. 6b. The line 4x + 2y = 4 is transformed by a dilation with the scale factor of 3 and centered at point (1, 0). Write the linear equation of its image. 6c. The line 4x + 2y = 4 is transformed by a dilation with the scale factor of 3 and centered at point (-2, -2). Write the linear equation of its image.

5 Name: Period: Date: : Properties of Dilations and Equations of lines Classwork 1. Identify the slope on each given equation a. 2x 4y = 12 b. 3y = 12 2x c. 3y + 2x = 9 d. 3x + 2y = 5 2. Line y = 2x 1 is transformed by a dilation with a scale factor of 2 and centered at origin. Write the equation of line s image 3. Line y = 2x 1 is transformed by a dilation with a scale factor of 2 and centered at (1,-3). Write the equation of line s image 4. The line 3y = 5 2x is transformed by a dilation centered at the origin. Which linear equation could be its image? a. 2x 3y = 8 b. 3x + 2y = 8 c. 3x 2y = 8 d. 3y + 2x = 8

6 Name: Period: Date: 5. The line 3x + 2y = 3 is transformed by a dilation with the scale factor of 3 and centered at point (0, 1). Write the linear equation of its image. 6. The line 2y = 3x + 6 is transformed by a dilation with the scale factor of 3 and centered at point (0, 0). Write the linear equation of its image. 7. The line 2y = 3x + 6 is transformed by a dilation with the scale factor of 3 and centered at point (0, -3). Write the linear equation of its image.

Lesson 26: Characterization of Parallel Lines

Lesson 26: Characterization of Parallel Lines Student Outcomes Students know that when a system of linear equations has no solution, i.e., no point of intersection of the lines, then the lines are parallel. Lesson Notes The discussion that begins