what's dilation

Question

 Triangle ABC has vertices A(-2,0), B(0,3), C(2,3) and is  dilated by a factor of 2 using the point (0,-1) as the point   of dilation. The dilated triangle is named A'B'C'. What are the coordinates of the vertices of the resulting triangle?

Answer 1

Dilation changes the size of the object while keeping the object shape.  Dilating by a factor of 2 makes an object twice as big.  It's a two step process:

 

First, subtract the point of dilation (P = (0,-1)) from each point on the triangle:

     A" = A - P = (-2-0,0-(-1)) = (-2,1)

     B' = ?

     C' = ?

 

Second, multiply by the dilation factor (2):
     A' = 2·A" = (2·(-2), 2·1) = (-4,2)

     B' = 2·B" = ?

     C'= 2·C" = ?

 

For more information, check out the following Wyzant study guide: https://www.wyzant.com/resources/files/629425/geometric_transformations_revised_11_2017