The points plotted on the coordinate plane below are three verticals of a rectangle?
What are the coordinates of the fourth vertex of the rectangle?
(2,3), (2,7), (6,7)
The fourth vertex of the rectangle would be (6,3).
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What are the coordinates of the fourth vertex of the rectangle (-1,-2.5) (-2,-2.5) (-2.5,-1) (-2.5,-2)
The rectangle has sides parallel to the x-axis and the y-axis. Therefore, the fourth vertex must be obtained by switching the x-coordinate or the y-coordinate of one of the given vertices.
We can see that the first two vertices have the same y-coordinate, and the last two vertices have the same x-coordinate. Therefore, we can switch the x-coordinate of the first or second vertex with the x-coordinate of the third or fourth vertex, or we can switch the y-coordinate of the third or fourth vertex with the y-coordinate of the first or second vertex.
To obtain a rectangle with positive x- and y-coordinates, we can switch the x-coordinate of the first vertex with the x-coordinate of the fourth vertex:
(-1,-2.5) (-2,-2.5) (-2.5,-1) (-2.5,-2)
Switch the x-coordinate of (-1,-2.5) with the x-coordinate of (-2.5,-2) to obtain:
(-2.5,-2.5) (-2,-2.5) (-2.5,-1) (-1,-2)
Therefore, the fourth vertex of the rectangle is (-1,-2).
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what the question to the points plotted on the coordinate plane below are three vertices of a rectangle
"What are the coordinates of the fourth vertex of the rectangle?" would be an appropriate question to ask if the points plotted on the coordinate plane are three vertices of a rectangle.
To find the coordinates of the fourth vertex of the rectangle, we need to use the properties of rectangles.
Since the given points are three vertices of the rectangle and they are all vertical, we can determine the coordinates of the fourth vertex by finding the reflection of one of the given points across the line of symmetry.
To do this, we can consider that opposite sides of a rectangle are parallel and of equal length. We can find the length of one side of the rectangle by calculating the difference between the y-coordinates of two adjacent points.
Let's say the given coordinates are (x1, y1), (x2, y2), and (x3, y3). The difference in the y-coordinates of two adjacent points will give us the length of the rectangle's side.
Length of side = |y2 - y1|
Now, we can calculate the coordinates of the fourth vertex using the given points. Let's say the fourth vertex is (x4, y4).
If (x1, y1) and (x2, y2) are adjacent points, then (x4, y4) can be obtained by performing the following reflections:
1. Reflect (x2, y2) across the y-axis to get (-x2, y2).
2. Reflect (-x2, y2) across the x-axis to get (-x2, -y2).
Similarly, if (x2, y2) and (x3, y3) are adjacent points, then (x4, y4) can be obtained as:
1. Reflect (x3, y3) across the y-axis to get (-x3, y3).
2. Reflect (-x3, y3) across the x-axis to get (-x3, -y3).
Therefore, the possible coordinates of the fourth vertex of the rectangle can be (-x2, -y2) or (-x3, -y3), depending on which pair of adjacent points we choose.
Note: It is also possible to have multiple rectangles with the given set of points. In this case, there will be multiple possible coordinates for the fourth vertex.