Locating the Center of Dilation
Grade 7 students in Big Ideas Math Advanced 2 (Chapter 2: Transformations) learn to locate the center of dilation by drawing lines through corresponding vertices of a pre-image and its dilated image. All such lines intersect at one point—the center of dilation—which acts like a flashlight source.
Key Concepts
Property If you are looking at a pre image and its dilated image, you can work backwards to find the exact Center of Dilation. Because dilations expand outward in straight lines, drawing straight lines through corresponding vertices (connecting A to A', B to B', C to C', and extending them) will eventually make all the lines intersect at one single point. That intersection is the Center of Dilation.
Examples Finding the Center: You have a small square PQRS and a large square P'Q'R'S'. Place a ruler on point P and point P', draw a long line. Do the same for Q and Q'. The exact spot on the graph where those two lines cross each other is your center of dilation.
Explanation Think of the Center of Dilation as a flashlight, and the shape as an object casting a shadow. The light rays travel in perfectly straight lines through the corners of the object to create the enlarged shadow. By tracing the lines backwards from the shadow (image) through the object (pre image), you will always find the flashlight (center). If you draw the lines and they are perfectly parallel and never cross, then the shape wasn't dilated—it was translated!
Common Questions
How do you find the center of dilation in 7th grade?
Draw lines connecting each vertex of the pre-image to its corresponding image vertex and extend them. All lines intersect at one point, which is the center of dilation.
What is the center of dilation?
The center of dilation is the fixed point from which all dilations expand or contract. Every point of the figure moves along a straight line through this center.
How can you tell if a transformation is a dilation vs a translation?
Draw lines through corresponding vertices. If the lines converge at one point, the transformation is a dilation. If the lines are parallel and never intersect, it is a translation.
What chapter in Big Ideas Math Advanced 2 covers locating the center of dilation?
Chapter 2: Transformations in Big Ideas Math Advanced 2 (Grade 7) covers locating the center of dilation.
What happens to the center of dilation point itself during dilation?
The center of dilation remains fixed. It is the only point that does not move during a dilation.