Dilations on the Coordinate Plane & Informal Proofs of Properties - 8.3 - Lessons 6 and 7

Student Outcomes

1. Students describe the effect of dilations on two-dimensional figures using coordinates (Lesson 6).

2. Students know an informal proof of why dilations are degree-preserving transformations and map segments to segments, lines to lines, and rays to rays.

Lesson Review

-We know that we can calculate the coordinates of a dilated point given the coordinates of the original point and the scale factor. 

-To find the coordinates of a dilated point we must multiply both the -coordinate and the -coordinate by the scale factor of dilation.

-If we know how to find the coordinates of a dilated point, we can find the location of a dilated triangle or other two dimensional figure. 

Lesson Summary 

• Dilation has a multiplicative effect on the coordinates of a point in the plane.   Given a point  in the plane, a dilation from the origin with scale factor  moves the point  to
• For example, if a point  in the plane is dilated from the origin by a scale factor of , then the coordinates of the dilated point are

Remember:  In order to dilate an object and make it bigger, you need to multiply by a scale factor that is greater than 1.

In order to dilate an object and make it smaller, you need to multiply by a scale factor that is a fraction greater than 0 but less than 1.