SOLUTION: Points R(1, 3), S(�2, �1), and T(5, �1) are vertices of a parallelogram. Give the coordinates of three possible points of the other vertex.

Question 1094441: Points R(1, 3), S(�2, �1), and T(5, �1) are vertices of a parallelogram. Give the coordinates of three possible points of the other vertex.

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Points and define a horizontal segment ST,
with a length of units.
units to the left of , at U,
or units to the right of , at V.
with an x-coordinate of either or ,
and of course the same as point R.
So, and are two of the possible locations of the fourth vertex.
Those two options give you parallelograms SURT and SRVT, shown below.
and
If ST is a diagonal, then RT and RS are sides,
R is above diagonal ST, and fourth vertex W is below the diagonal
with SW parallel to RT,
SW slanting down from , just as RT slants down from R,
going units down,
and units to the right.
That gives us ,
and ,
and puts the fourth vertex at .
With W, you form parallelogram SWTR, shown below.

RELATED QUESTIONS
The points (5,2), (2,6), and (-8,-3) are three vertices of a parallelogram. Locate and... (answered by venugopalramana,bwpbruce)

In the diagram, three vertices of parallelogram ORST are O(0, 0), R(b, d), and T(a,0).... (answered by Edwin McCravy)

Three of the vertices of a parallelogram are (2, 1) (4, 7), and (6, 5). What are the... (answered by KMST)

Show that the points (1,-3),(4,3),(3,7) and (0,-1) are vertices of a... (answered by Alan3354)

The points A(0,0), B(2,4)and D(7,O) are three of the four vertices of a parallelogram.... (answered by solver91311)

Show that the points (-1, -3) (-2, 0) (1, 6) and (2, 3) are the vertices of a... (answered by Boreal)

Points X (-1,1),Y (3,5), and Z (17,1), are the coordinates of three vertices of a... (answered by psbhowmick,MathLover1)

The coordinates of three vertices of a parallelogram are (−3, 3), (2, 3), and (4,... (answered by MathLover1)

QRST is a parallelogram. Parallelogram QRST with points: Q = (0, 0), R = (a, b), S = (?,... (answered by xachu4u)