Final answer:
To find the fourth point of a parallelogram with given points (4,3), (-4,3), and (2,-3), we use vector addition and the properties of parallelograms. We identify vectors formed by the points, apply the parallelogram rule, and determine that the coordinates of the fourth point are (10, -3).
Step-by-step explanation:
The student is asking for the coordinates of the fourth point to complete a parallelogram given three other points. To find the fourth point, we can use the concept of vector addition. The given points are (4,3), (-4,3), and (2,-3). We can think of these points as vectors from the origin. To form a parallelogram, opposite sides are parallel and equal in length.
First, let's consider the vectors formed by the given points:
- Vector 1: from (-4,3) to (4,3) which is (4 - (-4), 3 - 3) = (8, 0)
- Vector 2: from (-4,3) to (2,-3) which is (2 - (-4), -3 - 3) = (6, -6)
Applying the parallelogram rule, we add vector 1 to the third point (2,-3) to find the fourth point:
- Fourth Point: (2 + 8, -3 + 0) = (10, -3)
Therefore, the coordinates of the fourth point are (10, -3).