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Line Dilations Exploration

Autor:Tulya Garcia-Olteanu, siegel.benjamin1

Linear Dilations Exploration Instructions

In this exploration you will be exploring the relationship between the equations of dilated lines. We will ask you to see the effect that changing either the scale factor (k) or the center of dilation (point D) has on the equations of the pre-image. After performing each dilation, please convert each equation into slope-intercept form and then write your answer to the question.

Pre-work

The equation of the pre-image is -2x+3y = 9; rewrite this in slope-intercept form.

Prework Question

What is the slope and y-intercept of the pre-image?

Case 1: Dilation centered around the origin.

Please move the center of dilation to the origin, then change the scale factor to a integer value of your choice. Write down the equation of the image and put it into slope intercept form.

Case 1 Question 1

What happened to the slope? What happened to the y-intercept?

Case 1 Question 2

WITHOUT USING THE GEOGEBRA GRAPH (we will know if you are lying to us. We always know), what would you expect the equation of the line y = 2x + 3 to be after a dilation centered at the origin with a scale factor of 3?

Case 2: Dilation centered on the line

Please move the center of dilation to a point on the line, then change the scale factor to a integer value of your choice. Write down the equation of the image and put it into slope intercept form.

Case 2 Question 1

What happened to the slope? What happened to the y-intercept?

Case 2 Question 2

WITHOUT USING THE GEOGEBRA GRAPH (we will know if you are lying to us. We always know), what would you expect the equation of the line y = 2x + 3 to be after a dilation centered on the line with a scale factor of 3?

Case 3: Dilation not centered on the origin or line

Please move the center of dilation anywhere on the coordinate plane that is NOT the origin or a point on the line, then change the scale factor to a integer value of your choice. Write down the equation of the image and put it into slope intercept form.

Case 3 Question 1

What happened to the slope? What happened to the y-intercept?

Case 3 Question 2

WITHOUT USING THE GEOGEBRA GRAPH (we will know if you are lying to us. We always know), what would you expect the equation of the line y = 2x + 3 to be after a dilation centered at point (1,3) with a scale factor of 3?

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