Question 1070634: If point A(6,1),B (8,2),C (8,4),D (p,3) are vertices of a parallelogram taken in order, find value of p
Found 2 solutions by stanbon, MathTherapy:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! If point A(6,1),B (8,2),C (8,4),D (p,3) are vertices of a parallelogram taken in order, find value of p
------------------
Plot the 3 given points so you can see where the 4th
point would have to be.
------
AC is parallel to BD
AC has a slope of (4-1)/(8-6) = 3/2
----
So BD must have a slope of 3/2
slope of BD :: (3-2)/(p-8) = 3/2
1/(p-8) = 3/2
3p-24 = 2
3p = 26
p = 8 2/3
------------------------
Cheers,
Stan H.
------------
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website! If point A(6,1),B (8,2),C (8,4),D (p,3) are vertices of a parallelogram taken in order, find value of p
AB ∥ DC and BC ∥ AD
BC is a VERTICAL line that's parallel to the y-axis, and parallel and congruent to AD. BC's length = 4 - 2, or 2
AD is a VERTICAL line that's parallel to the y-axis, and parallel and congruent to BC. Points A and D will therefore have the SAME x-coordinate, which is 6.
Therefore, p = 6.
OR
You can also see that AB and DC are parallel, and so, have the same slope. Slope of AB = 
DC's slope also =  .
To find p, we get: 
|
|
|
