Final answer:
Upon plotting on a coordinate plane, we observe that quadrilateral EFGH has opposite sides equal and parallel with horizontal and vertical sides, indicating it is a rectangle, the most precise name for the quadrilateral.
Step-by-step explanation:
To graph the quadrilateral with vertices E(-3, 1), F(-7, -3), G(6, -3), and H(2, 1), you would first plot each point on a coordinate plane. Connect the points in sequence to form the quadrilateral EFGH. By examining the lengths of the sides and the angles, we can determine the most precise name for the quadrilateral.
First, observe that EF and GH are both horizontal lines and FG and EH are both vertical lines. This suggests that opposite sides are parallel, indicating that EFGH is a parallelogram. Second, measure the lengths of EF and GH to see if they are equal, and do the same with FG and EH. If all sides are equal in length, EFGH is a rhombus. If only opposite sides are equal, it is a rectangle. To determine if EFGH is a square, verify if all sides are equal and all angles are right angles.
Based on the coordinates, EF = GH = 10 units and FG = EH = 9 units. Therefore, the opposite sides are equal and parallel, but not all sides are of equal length, so EFGH is a rectangle. If EFGH had four right angles, which is a characteristic of rectangles, then the most precise name for the quadrilateral is a rectangle. Since we are working with a coordinate plane, we can assume right angles where the sides meet, making a rectangle the most precise name.
To summarize, after plotting the points and connecting them to form a quadrilateral, we can conclude that the figure is a rectangle, as opposite sides are equal and parallel, and each angle appears to be a right angle based on the orientation of the sides.