Final answer:
To find the coordinates of the fourth vertex of a rectangle, we need to find the vector that connects the second and third vertices and add it to the coordinates of the first vertex. Given the coordinates (4,3), (-4,3), and (-4,-2) of three vertices, the coordinates of the fourth vertex are (4, -2).
Step-by-step explanation:
To find the coordinates of the fourth vertex of a rectangle, we need to understand that a rectangle has two sets of parallel sides. The opposite sides of a rectangle are parallel and of equal length. So, to find the fourth vertex, we need to find the vector that connects the second and third vertices and add it to the coordinates of the first vertex.
Given the coordinates (4,3), (-4,3), and (-4,-2) of three vertices, the vector between the second and third vertices is (-4-(-4), -2-3) = (0, -5). Adding this vector to the coordinates of the first vertex (4,3), we get (4+0, 3+(-5)) = (4, -2).
Therefore, the coordinates of the fourth vertex are (4, -2).