MATH SOLVE

2 months ago

Q:
# 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.

Accepted Solution

A:

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)