Using Equations for Lines
5 min
Teacher Prep
Setup
Required Preparation
Narrative
The purpose of this activity is to revisit the meaning of dilations and the fact that the center of dilation, the point dilated, and the image all lie on the same line.
Launch
Provide access to geometry toolkits. Give students 1–2 minutes of quiet work time followed by a whole-class discussion.
Student Task
A dilation with scale factor 2 sends A to B. Where is the center of the dilation?
Sample Response
Sample response: The center of dilation is on the same line as A and B, the same distance from B to A, but on the other side of A.
Activity Synthesis (Teacher Notes)
The goal of this discussion is to review key ideas about dilations. Ask students:
-
“What do you know about centers of dilations that helped you solve this problem?” (The center of dilation always lies on the same line as a dilated point and its image.)
-
“What do you know about scale factors that helped you solve this problem?” (The scale factor is 2, so the distance from the center to B had to be twice the distance from the center to A.)
Standards
- 8.G.A·Understand congruence and similarity using physical models, transparencies, or geometry software.
- 8.G.A·Understand congruence and similarity using physical models, transparencies, or geometry software.
15 min
15 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Using Equations for Lines
5 min
Teacher Prep
Setup
Required Preparation
Narrative
The purpose of this activity is to revisit the meaning of dilations and the fact that the center of dilation, the point dilated, and the image all lie on the same line.
Launch
Provide access to geometry toolkits. Give students 1–2 minutes of quiet work time followed by a whole-class discussion.
Student Task
A dilation with scale factor 2 sends A to B. Where is the center of the dilation?
Sample Response
Sample response: The center of dilation is on the same line as A and B, the same distance from B to A, but on the other side of A.
Activity Synthesis (Teacher Notes)
The goal of this discussion is to review key ideas about dilations. Ask students:
-
“What do you know about centers of dilations that helped you solve this problem?” (The center of dilation always lies on the same line as a dilated point and its image.)
-
“What do you know about scale factors that helped you solve this problem?” (The scale factor is 2, so the distance from the center to B had to be twice the distance from the center to A.)
Standards
- 8.G.A·Understand congruence and similarity using physical models, transparencies, or geometry software.
- 8.G.A·Understand congruence and similarity using physical models, transparencies, or geometry software.