To graph: The parallelogram PQRS where coordinates of the point P, Q and R are . Also compute the coordinate of the point Q .
PQRS is a parallelogram and coordinates of three points are .
Plot the points on the coordinate plane.
Let the coordinates of the point S be .
It is known that diagonals of the parallelogram bisect each.
The parallelogram has two diagonals and .
Let be the midpoint of the diagonal joined by the line segment .
Recall that the midpoint of the segment that joins two points in the Cartesian plane is denoted by .
Now, is the mid-point of the line segment joined by the points .
Therefore, is the mid-point of the line segment joined by the points .
Also, is the mid-point of the line segment joined by the points .
Equate the x -coordinate of each bracket,
Equate the y -coordinate of each bracket,
Therefore, coordinates of the point S are .
Now, plot the points on the coordinate plane.
The parallelogram PQRS so formed above, has diagonals that bisect each other. Opposites sides are congruent. Opposite angles are congruent. Consecutive angles are supplementary that is adds to .
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