Write the co-ordinate of the vertices of a rectangle whose length and breadth are 6 and 3 units respectively, one vertex at origin, the longer side lies on the y axis and one of the verteces lies in the second quadrant. please answer me question (i rate us brain least and like and points 100)
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Answer: Second Quadrant
Step-by-step explanation:
Vertex 1: (0, 0)
Vertex 2: (0, 3√3)
Vertex 3: (-3, 3√3)
Vertex 4: (-3, 0)
These coordinates satisfy the given conditions, with one vertex at the origin, the longer side lying on the y-axis, and one vertex in the second quadrant.
Step-by-step explanation:
Sure, I'd be happy to help! Let's start by understanding the given information:
1. The rectangle has a length of 6 units and a breadth of 3 units.
2. One vertex is at the origin (0, 0).
3. The longer side of the rectangle lies on the y-axis.
4. One of the vertices lies in the second quadrant.
Given this information, let's proceed to find the coordinates of the other three vertices.
Since one vertex is at the origin (0, 0), let's find the coordinates of the other three vertices using the length and breadth of the rectangle.
Let's start by finding the coordinates of the vertex on the y-axis:
- Since the longer side lies on the y-axis, the x-coordinate of this vertex will be 0.
- The y-coordinate can be determined by using the length of the rectangle, which is 6 units.
- So, the coordinates of this vertex will be (0, 6).
Now, let's find the coordinates of the vertex in the second quadrant:
- The x-coordinate of this vertex will be negative since it's in the second quadrant.
- The y-coordinate can be determined by using the breadth of the rectangle, which is 3 units.
- So, the coordinates of this vertex will be (-3, y).
Now, since the rectangle is symmetric about the y-axis, the y-coordinate of the vertex in the second quadrant will be the same as the y-coordinate of the vertex on the y-axis, which is 6 units.
Therefore, the coordinates of the vertex in the second quadrant are (-3, 6).
To summarize, the coordinates of the four vertices of the rectangle are:
1. Origin: (0, 0)
2. On y-axis: (0, 6)
3. Vertex on y-axis and in the second quadrant: (0, 6)
4. Vertex in the second quadrant: (-3, 6)
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