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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Step-by-step explanation:

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq

is should be y = 5x

step-by-step explanation:

correct me if im wrong