Parallelogram abcd is dilated to form parallelogram a'b'c'd'. describe the dilation used to create the image.

Parallelogram ABCD is dilated by scale factor 1.5 and center origin

Step-by-step explanation:

* Lets explain how to solve the problem

- A dilation is a transformation that produces an image that is the

 same shape as the original, but is a different size

- A dilation stretches or shrinks the original figure

- A dilation has scale factor and center of the dilation

- The figure and its image by dilation are similar, that means there

 corresponding angles are equal in measures and their corresponding

 sides are proportion

* Lets solve the problem

- ABCD is a parallelogram is dilated to form parallelogram A'B'C'D'

- The vertices of ABCD are A (-8 , -1) , B (-6 , 2) , C (-3 , 2) , D (-5 , -1)

- The vertices of A'B'C'D' are A' (-12 , -1.5) , B' (-9 , 3) , C' (-4.5 , 3) ,

  D' (-7.5 , -1.5)

- To find the scale factor of dilation find the length of two

  corresponding sides in the two parallelograms and divide them

∵ Side AD is a horizontal side

∴ Its length is the difference between the x-coordinates of points

  A and D

∵ x-coordinate of point A = -8

∵ x-coordinate of point D = -5

∴ AD = (-5) - (-8) = -5 + 8 = 3

∴ The length of side AD is 3 units

∵ Side A'D' is a horizontal side

∴ Its length is the difference between the x-coordinates of points

  A' and D'

∵ x-coordinate of point A' = -12

∵ x-coordinate of point D = -7.5

∴ AD = (-7.5) - (-12) = -7.5 + 12 = 4.5

∴ The length of side A'D' is 4.5 units

∵ The scale factor of dilation = A'D'/AD

∴ The scale factor of dilation = 4.5/3 = 1.5

∴ The scale factor of dilation is 1.5

- The center of dilation is the origin if the origin , the point

  and the image of the point are colinear

∵ The slope of the line OC = y/x = 2/-3 = -2/3

∵ The slope of the line OC' = y/x = 3/-4.5 = -2/3

∵ OC and OC' have same slops

∴ O , C and C' are collinear

∴ The origin is the center of dilation

∴ Parallelogram ABCD is dilated by scale factor 1.5 and center origin

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