Answer:
AD = 4 units
C(3, -10)
D(-7, -10)
Step-by-step explanation:
The midpoint of a line segment is the point that is exactly halfway between its two endpoints. Given that the midpoint of line segment AD is located 2 units down from A, it tells us that D must be directly below A along the same vertical line, making AD a vertical line segment. Therefore, D is 4 units below A, and the length of AD is:
[tex]\sf \overline{\sf AD}=4\;units[/tex]
Since A and D are on the same vertical line, the x-coordinate of D is the same as the x-coordinate of A, and the y-coordinate of D can be found by subtracting 4 from the y-coordinate of A. Therefore, the coordinates of vertex D are:
[tex]\sf D=(-7,-6-4)\\\\D=(-7,-10)[/tex]
Since ABCD is a rectangle and points A(-7, -6) and B(3, -6) are on the same horizontal line (having the same y-coordinate), and points A(-7, -6) and D(-7, -10) are on the same vertical line (having the same x-coordinate), the x-coordinate of C will be the same as B, and the y-coordinate of C will be the same as D. Therefore, the coordinates of vertex C are:
[tex]\sf C=(3,-10)[/tex]
