Answer:
(0, -1)
Step-by-step explanation:
A parallelogram is a quadrilateral (has four sides) in which opposite sides are parallel to each other. Also for a parallelogram, the opposite sides and angles are equal to each other.
Hence for parallelogram RSTU, RS // TU and RU // ST
Let the coordinate of U be (x , y). Two lines are parallel to each other if their slopes are equal, hence:
Slope of RS = (4 - 1) /[3 - (-3)] = 3/6 = 0.5
Slope of ST = (2 - 4) /[6 - 3] = -2/3
Slope of RU = (y - 1) /[x - (-3)] = (y - 1) / (x + 3)
Slope of TU = (y - 2) /[x - 6]
Slope of RU = Slope of ST
(y - 1) / (x + 3) = -2/3
3y - 3 = -2x -6
2x + 3y = -6 + 3
2x + 3y = -3 (1)
Slope of RS = Slope of TU
0.5 = (y - 2) /[x - 6]
0.5x - 3 = y - 2
0.5x - y = 1 (2)
Solving 1 and 2 simultaneously gives:
x = 0, y = -1
Therefore the coordinates of U = (0, -1)
