The point plotted on the coordinate plane are three vertices of a rectangle. What are the coordinates of the fourth vertex of the rectangle?
Without additional information, it is impossible to determine the exact coordinates of the fourth vertex. However, we can use the properties of rectangles to narrow down the possibilities.
Recall that a rectangle has two pairs of parallel sides, and all angles are right angles. This means that the distance between the x-coordinates of the two vertices on one side must be the same as the distance between the x-coordinates of the two vertices on the opposite side. Similarly, the distance between the y-coordinates of the two vertices on one side must be the same as the distance between the y-coordinates of the two vertices on the opposite side.
Using this information, we can calculate the possible x- and y-coordinates of the fourth vertex. Let's say that the three given vertices are (x1, y1), (x2, y2), and (x3, y3). If (x1, y1) and (x2, y2) form a side of the rectangle, then the other side parallel to it must be formed by (x3, y3) and some unknown point (x4, y4). We can use the distance formula to find the distance between (x1, y1) and (x2, y2), and then add or subtract that distance from x3 and y3 to find the possible x- and y-coordinates of (x4, y4).
For example, if (x1, y1) = (0, 0), (x2, y2) = (0, 2), and (x3, y3) = (2, 0), then the distance between (x1, y1) and (x2, y2) is 2. Therefore, the possible coordinates of the fourth vertex (x4, y4) are (2, 2) and (2, -2), since those are the points that are 2 units away from (2, 0) along a vertical line.
Note that this method only works if we know for sure that the given points form a rectangle (i.e. if they satisfy the conditions of having two pairs of parallel sides and all right angles). If the given points do not form a rectangle, then it is impossible to find the coordinates of the fourth vertex based on the given information alone.