Using properties of parallelograms, RSTU is a parallelogram that has vertices R (-3,1), S (3,4), and T( 6,2(. What are the coordinates of point U.

(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)