If the vertices of a parallelogram PQRS taken in order are P(3,4), Q(-2,3) and R(-3,-2),then the coordinates of its fourth vertex S are

To find the coordinates of the fourth vertex S of the parallelogram PQRS, we can use the fact that opposite sides of a parallelogram are parallel and equal in length.

Step 1: Find the vector representing the direction from P to Q.

• The vector from P to Q is given by (x2 - x1, y2 - y1) = (-2 - 3, 3 - 4) = (-5, -1).

Step 2: Add this vector to the coordinates of R to find the coordinates of S.

• The coordinates of S can be found by adding the vector (-5, -1) to the coordinates of R (-3, -2).
• Adding the corresponding components, we get: x-coordinate of S = -3 + (-5) = -8, and y-coordinate of S = -2 + (-1) = -3.

Therefore, the coordinates of the fourth vertex S are (-8, -3).