If pentagon opqrs is dilated by a scale factor of seven over four from the origin to create o'p'q'r's', what is the ordered pair of point q'? if o negative 1, 2, at p negative 5, 3, at q negative 3, negative 2, at r 2, 1, and at s 2, 5.

The order pair of point Q' is (-21/4 , -7/2)

Step-by-step explanation:

* Lets explain the dilation

- A dilation is a transformation that changes the size of a figure.  

- The figure can become larger or smaller, but the shape of the

 figure does not change.  

- The scale factor, measures how much the image will be larger

 or smaller  

- If the scale factor greater than 1, then the image will be larger

- If the scale factor between 0 and 1, then the image will be smaller

- The center of dilation is a fixed point in the plane about which all

 points are expanded or contracted

* Lets solve the problem

- The pentagon OPQRS is dilated by a scale factor 7/4

- The center of dilation is the origin

- The image of the pentagon after the dilation is O'P'Q'R'S'

∵ The coordinates of the vertices of the pentagon OPQRS are

  O (-1 , 2) , P (-5 , 3) , Q (-3 , -2) , R (2 , 1) , S (2 , 5)

- To find the image of each point after the dilation multiply each

  coordinates of the points by the scale factor of dilation

∵ The scale factor is 7/4

∵ The coordinates of point Q are (-3 , -2)

∴ The image of point Q after dilation is (-3 × 7/4 , -2 × 7/4)

∴ The image of point Q after dilation is (-21/4 , -7/2)

∵ Q' is the image of Q

∴ Q' = (-21/4 , -7/2)

* The order pair of point Q' is (-21/4 , -7/2)

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step-by-step explanation:

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