PQRS is a rectangle. One side is on the X axis, vertex s is located at (5.4) state two possibilities for coordinates for the other vertices.
You mean (5 , 4) I hope.
Draw it.
eg
(5,0), (0,0) , (0,4) and our (5,4)
or
(5,0), (10,0) , (10,4) and our (5,4)
To find the possibilities for the coordinates of the other vertices of rectangle PQRS, we need to consider the properties of a rectangle.
1. The opposite sides of a rectangle are equal in length and parallel. Therefore, the length of PS will be equal to the length of QR.
2. One side of the rectangle is on the x-axis. Since vertex S is located at (5,4), we can assume that PQ is parallel to the x-axis.
Based on these properties, we can consider two possibilities for the coordinates of the other vertices:
Possibility 1:
- Let's assume that the length of QR is 2. In this case, the coordinates of the other vertices would be:
- Q: (5, 2)
- R: (7, 4)
Possibility 2:
- Let's assume that the length of QR is 3. In this case, the coordinates of the other vertices would be:
- Q: (5, 1)
- R: (8, 4)
These are two possible sets of coordinates for the other vertices of rectangle PQRS, considering the given conditions.
To find two possibilities for the coordinates of the other vertices of the rectangle PQRS, we need to consider the properties of a rectangle.
In a rectangle, opposite sides are equal in length, and the adjacent sides are perpendicular to each other. Additionally, if one side of the rectangle lies on the X axis, the opposite side will lie on the Y axis.
Given that vertex S is located at (5,4) on the X axis, we can consider the two possibilities for the coordinates of the other vertices:
1. Possibility 1: The opposite side of the rectangle (PQ) lies on the Y axis. If PQ is perpendicular to the X axis, then P must have the same X-coordinate as S (5), but the Y-coordinate is different. For example, P could be located at (5,7).
P (5,7)
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S (5,4)
2. Possibility 2: The adjacent side of the rectangle (PR) lies on the Y axis. If PR is perpendicular to the X axis, then R must have the same Y-coordinate as S (4), but the X-coordinate is different. For example, R could be located at (8,4).
R (8,4)
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S (5,4) —— P (5,?)
These are two possible sets of coordinates for the other vertices of the rectangle PQRS. Note that without additional information, such as the length of PQ or PR, or any specific angles, we cannot determine the exact coordinates of the other vertices, only possibilities.