Unit 2, Lesson 12
Using Equations for Lines
Grade 8
12.1
Warm-up
A dilation with scale factor 2 sends to . Where is the center of the dilation?
12.2
Activity
Here is triangle .
- Draw the dilation of triangle with center and scale factor 2.
- Draw the dilation of triangle with center and scale factor 2.5.
- For which scale factor does the dilation with center send point to ? Explain your reasoning.
- What are the coordinates of point after a dilation with center and scale factor ?
12.3
Activity
Here is a line.
- Using what you know about similar triangles, find an equation for the line in the diagram.
- What is the slope of this line? Does it appear in your equation?
- Is also on the line? Explain your reasoning.
- Is also on the line? Explain your reasoning.
Student Lesson Summary
Here is a line with a few of the points labeled.
We can use what we know about slope to decide if a point lies on a line.
First, use points and slope triangles to write an equation for the line.
- The slope triangle with vertices and gives a slope of .
- The slope triangle with vertices and gives a slope of .
- Since these slopes are the same, is an equation for the line.
To check whether or not the point lies on this line, we can check that . Since is a solution to the equation, it's on the line!
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