SOLUTION: P(-1,-2), Q(5,k), R(8,2), S(h,1) are the four vertices of the parallelogram PQRS, Find the value of h, and the value of k.

Question 945242: P(-1,-2), Q(5,k), R(8,2), S(h,1) are the four vertices of the parallelogram PQRS, Find the value of h, and the value of k.
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

given:
P(,), Q(,), R(,), S(,) are the four vertices of the parallelogram ,
the parallelogram is quadrilateral with two pairs of and in length sides
is parallel and equal to
is parallel and equal to
distance from and is equal to distance from to
and
distance from and is equal to distance from to
Now use the distance formula to find the distance between the two points, P(,) and Q(,):

=> this is also equal to distance from R(,) to S(,)

since is parallel and equal to , we have
......square both sides

........eq.1

now find the distance between the two other points Q(,) and R(,)

then, between the two other points P(,) and S(,)

so,

........eq.2
solve the system:
........eq.1
........eq.2
-------------------------------------------subtract 2 from 1

...solve for

.............substitute in eq.1

........eq.1 ...solve for

.......use quadratic formula

or
we will use and find

so, we will have points:
P(,), Q(,), R(,), S(,)
now we can graph a parallelogram

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