Question

Three vertices of a parallelogram have coordinates (0, 1), (3, 7), and (4, 4). what are the coordinates of the fourth-quadrant vertex?

Answer 1

To solve this problem you must apply the proccedure shown below:

 Points: A(0, 1), B(3, 7), C(4, 4), D(x,y)
 1. You must make a system of equations by applying the slope formula:

 The slope AB=CD:

 (y-4)/(x-4)=(7-1)/(3-0)
 3y=6x-12  (First equation)

 The slope of AD=BC:
 
 (y-1)/(x-0)=(4-7)/(4-3)
 y=-2 (Second equation)

 2. When you solve it, you obtain:

 x=1
 y=-2

 The answer is: (1,-2)