Answer: (-1, 1)
Step-by-step explanation:
Let D represent the fourth vertex with coordinate (x, y)
Since ABCD is a rectangle, then BC || AD and AB || DC
Since BC is parallel to AD, then they have the same slope (m) = -1
Equation of line AD: y - (-2)) = -1(x - 2) ⇒ y + 2 = -x + 2 ⇒ y = -x
Since AB is parallel to DC, then they have the same slope (m) = 1
Equation of line DC: y - 7 = 1(x - 5) ⇒ y - 7 = x - 5 ⇒ y = x + 2
D is where the two lines intersect so the next step is to solve the system of equations: y = -x and y = x + 2
Using substitution method: -x = x + 2 ⇒ -2x = 2 ⇒ x = -1
Now solve for y: y = -x ⇒ y = -(-1) ⇒ y = 1
x = -1 and y = 1
