Final answer:
To form a rectangle with given points on a coordinate plane, the missing corner point must be found with consistent x or y coordinates with the opposite corners. The missing fourth point for the rectangle with coordinates (-4,7), (-1,7), and (-4,-2) is (-1,-2), completing the rectangle when plotted on the graph.
Step-by-step explanation:
When plotting points in a coordinate plane to form geometrical shapes like rectangles, it is helpful to understand how to find the missing corner of the rectangle. We have been given three points to plot, (-4,7), (-1,7), and (-4,-2). To complete the rectangle, we need to find a fourth point that has the same y-coordinate as (-4,-2) and the same x-coordinate as (-1,7).
The first step is to plot the given points on the coordinate plane. You'll find that (-4,7) and (-1,7) are aligned horizontally, and (-4,-2) is vertically aligned with (-4,7), forming an 'L' shape. Since rectangles have opposite sides that are equal in length and are parallel, the missing point to create a rectangle with these three points would have the same y-coordinate as the point (-4,-2), which is -2, and the same x-coordinate as (-1,7), which is -1. Therefore, the fourth point would be (-1,-2).
After plotting all four points, you can draw straight lines connecting the adjacent points, forming the rectangle on the coordinate plane. Remember that in a coordinate system, the x-coordinate signifies the position along the horizontal axis, while the y-coordinate represents the position along the vertical axis.