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)