Using Equations for Lines: IM 8.2.12
[url=https://im.kendallhunt.com/MS/teachers/3/2/12/preparation.html]“Using Equations for Lines”[/url] from IM Grade 8 by [url=https://www.geogebra.org/m/gus8ffvr]Open Up Resources[/url] and Illustrative Mathematics. Licensed under the [url=https://creativecommons.org/licenses/by/4.0/]Creative Commons Attribution 4.0 license[/url].
Table of Contents
- Lesson 8.2.12
- IM 8.2.12 Lesson: Using Equations for Lines
- Practice 8.2.12
- IM 8.2.12 Practice: Using Equations for Lines
IM 8.2.12 Lesson: Using Equations for Lines
A dilation with scale factor 2 sends A to B. Where is the center of the dilation?
Here is a line.
Using what you know about similar triangles, find an equation for the line in the diagram. (You can use the applet above to help).
[size=150][size=100]What is the slope of this line? Does it appear in your equation?[/size][/size]
Is [math](9,11)[/math] also on the line?
How do you know?
Is [math](100,193)[/math] also on the line?
There are many different ways to write down an equation for a line like the one in the problem.
Does [math]\frac{y-3}{x-6}=2[/math] represent the line? Explain your reasoning.
What about [math]\frac{y-6}{x-4}=5[/math]? Explain your reasoning.
What about [math]\frac{y+5}{x-1}=2[/math]? Explain your reasoning.
Here is triangle ABC. Draw the dilation of triangle ABC with center (0,1) and scale factor 2.
Here is triangle ABC. Draw the dilation of triangle ABC with center (0,1) and scale factor 2.5.
Where is C mapped by the dilation with center (0, 1) and scale factor s?
For which scale factor does the dilation with center (0, 1) send C to (9, 5.5)?
Explain how you know.
IM 8.2.12 Practice: Using Equations for Lines
Select [b]all[/b] the points that are on the line through [math](0,5)[/math]and [math](2,8)[/math].
All three points displayed are on the line.
Find an equation relating [math]x[/math] and [math]y[/math].
Here is triangle ABC. Draw the dilation of triangle ABC with center (2,0) and scale factor 2.
Here is triangle ABC. Draw the dilation of triangle ABC with center (2,0) and scale factor 3.
Here is triangle ABC. Draw the dilation of triangle ABC with center (2,0) and scale factor 1/2.
What are the coordinates of the image of point [math]C[/math] when triangle [math]ABC[/math] is dilated with center [math](2,0)[/math] and scale factor [math]s[/math]?
Write an equation for the line containing all possible images of point [math]C[/math].
Here are some line segments.
Which segment is a dilation of [math]\overline{BC}[/math] using A as the center of dilation and a scale factor of [math]\frac{2}{3}[/math]?
Which segment is a dilation of [math]\overline{BC}[/math] using A as the center of dilation and a scale factor of [math]\frac{3}{2}[/math]?
Which segment is not a dilation of [math]\overline{BC}[/math], and how do you know?