Answer:
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)
