Final answer:
To graph the polygon with the given vertices Q(-6,-3), R(-5, 0), S(-3,0), and T(7,-1), plot each point on a Cartesian plane and connect them in order. To find the image after a clockwise rotation of 270 degrees about the origin, apply the rotation transformation to each vertex.
Step-by-step explanation:
To graph the polygon with the given vertices Q(-6,-3), R(-5, 0), S(-3,0), and T(7,-1), we plot each point on a Cartesian plane. Q is located 6 units to the left and 3 units down from the origin, R is located 5 units to the left and at the same level as the origin, S is located 3 units to the left and at the same level as the origin, and T is located 7 units to the right and 1 unit down from the origin. After plotting the points, we connect them in order to form the polygon.
To find the image of the polygon after a clockwise rotation of 270 degrees about the origin, we apply the rotation transformation to each vertex of the original polygon. Rotating a point (x, y) clockwise by 270 degrees is equivalent to rotating it counterclockwise by 90 degrees.
The new coordinates of each vertex can be found by applying the rotation transformation as follows:
Q' = (3, -6)
R' = (0, -5)
S' = (0, -3)
T' = (-1, 7)
After connecting the new vertices, we obtain the image of the polygon after the clockwise rotation.