SOLUTION: 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

Algebra.Com
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:

RELATED QUESTIONS

IF A(2,0),B(p,-2),C(-1,1) and D(3,r) are the vertices of a parallelogram ABCD,calculate... (answered by KMST)
If A(2 3) B(p -2) and C(-1 1) and D(3 r) are tthe vertices of a parallelogram ABCD... (answered by KMST)
The vertices of parallelogram ABCD are A(2, 4), B(0, 0), C(6, 2), and D(8, 6). Find the... (answered by ewatrrr)
Suppose that Parallelogram ABCD has vertices A(2, 4), B(8, 4), C(5, -3) and D(-1, -3).... (answered by KMST)
If the vertices of a parallelogram are (3,1), (8, 1), (6, 5), and (k, 5), a value of k... (answered by KMST)
If P(a,b),Q(a+3,b+4),R(a-1,b+7) are three vertices of a parallelogram PQRS,Find the... (answered by solver91311)
If P(a,b),Q(a+3,b+4),R(a-1,b+7) are three vertices of a parallelogram PQRS,Find the... (answered by solver91311)
4. Compute the probability. a. If P(A) = 0.2 , P(B)= 0.4, and P(A and B) = 0.1, find... (answered by ikleyn)
In an experiment, A, B, C, and D are events with probabilities P[A∪B]=5/8, P[A]=3/8,... (answered by mathprof)