Question

quadrilateral defg is dilated by a scale factor of 2 with a center (0, 0) then rotated 180 degrees counterclockwise. select from the drop - down menus to correctly complete the statement. if the quadrilateral is dilated by a factor of 2 with respect to the origin, rotated around the origin 180 degrees counterclockwise. the coordinate for the new f is (-16, -16)

Explanation:

Step1: Find the original coordinates of point F

From the graph, the original coordinates of point \( F \) are \( (8,8) \).

Step2: Apply the dilation

When dilating a point \( (x,y) \) by a scale factor \( k = 2 \) with respect to the origin, the new coordinates after dilation are \( (kx,ky) \). So for \( F(8,8) \), after dilation, the coordinates become \( (2\times8,2\times8)=(16,16) \).

Step3: Apply the rotation

When rotating a point \( (x,y) \) \( 180^{\circ} \) counter - clockwise around the origin, the transformation rule is \( (x,y)\to(-x,-y) \). For the point \( (16,16) \) after dilation, after rotation, the coordinates become \( (-16,-16) \).

Answer:

\((-16,-16)\)