A rectangle has vertices at these coordinates:
(2, −2), (2, 5), (−1, 5)
What are the coordinates of the fourth vertex of the rectangle?
Enter the coordinates by filling in the boxes.
(-1, -2)
To find the coordinates of the fourth vertex of the rectangle, we can use the fact that opposite sides of a rectangle are parallel.
Step 1: Identify two sides of the rectangle that are parallel. In this case, let's consider the sides formed by the points (2, -2) and (2, 5), and the points (-1, 5) and (the unknown fourth vertex).
Step 2: Calculate the difference between the x-coordinates and the y-coordinates of the points on the parallel sides.
For the x-coordinate, the difference is 2 - (-1) = 3.
For the y-coordinate, the difference is 5 - 5 = 0.
Step 3: Apply the difference to the known x-coordinate and y-coordinate of one of the endpoints of the parallel sides.
Let's use point (2, 5).
For the x-coordinate, add the difference to it: 2 + 3 = 5.
For the y-coordinate, add the difference to it: 5 + 0 = 5.
Therefore, the coordinates of the fourth vertex of the rectangle are (5, 5).
To find the coordinates of the fourth vertex of the rectangle, we can use the fact that opposite sides of a rectangle are parallel and equal in length.
Given three vertices of the rectangle:
- (2, -2)
- (2, 5)
- (-1, 5)
We can observe that the side between the first two vertices is vertical, and the side between the last two vertices is horizontal.
So, the fourth vertex should be the same distance horizontally from (-1, 5) as (-2, -2) is vertically from the same point.
Since (-2, -2) is 7 units vertically down from (2, 5), the fourth vertex should be horizontally 7 units to the left of (-1, 5).
Therefore, the coordinates of the fourth vertex of the rectangle are:
X-coordinate: -1 - 7 = -8
Y-coordinate: 5
So, the coordinates of the fourth vertex of the rectangle are (-8, 5).