SOLUTION: Please help me with this problem, I've been stuck on it for hours. Three consecutive vertices of a parallelogram are points (2, 4), (0, 0), and (6, 0). The fourth vertex is poin

Question 458400: Please help me with this problem, I've been stuck on it for hours.
Three consecutive vertices of a parallelogram are points (2, 4), (0, 0), and (6, 0). The fourth vertex is point
A)(2,-1)
b)(10,2)
C) (8,4)

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Three consecutive vertices of a parallelogram are points (2, 4), (0, 0), and (6, 0). The fourth vertex is point
---
Sketch the points on a coordinate system:
The missing point is at the intersection of two
lines: one is parallel to the x-axis and passes
thru (2,4); the other is parallel to the line
determined by (0,0)and(2,4).
------------------------
Let the missing point be (x,y):
The line parallel to the x-axis has equation y = 4
---------------------------------------------------------
The line parallel to the line thru (0,0)and(2,4)
has slope = 4/2 = 2 and passes thru (6,0)
Form: y = mx+b
0 = (2)(6) + b
b = -12
Equation: y = 2x-12
-----
You want the point where y = 4 and y = 2x-12 intersect.
Solve 4 = 2x-12
2x = 16
x = 8
-------
The point of intersection is (8,4)
=======================================
Cheers,
Stan H.
=========================

A)(2,-1)
b)(10,2)
C) (8,4)

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