Final answer:
To construct the parallelogram with the given information, draw the base segment connecting the two vertices, draw a perpendicular line segment with the length of the height from one vertex, draw a parallel line segment with the length of the height from the other vertex, and connect the endpoints of the parallel segments.
Step-by-step explanation:
The points (1,1) and (7,3) represent two vertices of a parallelogram. To construct the parallelogram, we can use the given information about the height and area. First, we draw a line segment connecting the two given points to represent the base of the parallelogram. Then, we draw a line segment perpendicular to the base from one of the vertices with a length of 6 units to represent the height of the parallelogram. Finally, we draw another line segment parallel to the base, also with a length of 6 units, from the other vertex. Connecting the endpoints of the two parallel line segments completes the construction of the parallelogram.