what is the coordinate of a rectangle with a vertex at (1,2) and dimensions 3 units by 4 units.....
If you put the 3 units along the x axis, the next corner is (4,2). The next corner goes at 4,6. You finish it.
To find the coordinates of the rectangle, we need to determine the coordinates of each vertex.
Given that one vertex is at (1, 2) and the dimensions of the rectangle are 3 units by 4 units, we can find the other three vertices as follows:
1. The top-right vertex: Since the width of the rectangle is 3 units, we add 3 units horizontally to the x-coordinate of the given vertex, and since the height is 4 units, we add 4 units vertically to the y-coordinate. Therefore, the top-right vertex has coordinates (1 + 3, 2 + 4) = (4, 6).
2. The bottom-left vertex: The bottom-left vertex will have the same x-coordinate as the given vertex and the y-coordinate reduced by the height of the rectangle. So, the bottom-left vertex has coordinates (1, 2 - 4) = (1, -2).
3. The bottom-right vertex: The bottom-right vertex will have the same y-coordinate as the bottom-left vertex and the x-coordinate increased by the width of the rectangle. Thus, the bottom-right vertex has coordinates (1 + 3, -2) = (4, -2).
The coordinates of all four vertices of the rectangle are:
- Vertex 1: (1, 2)
- Vertex 2: (4, 6)
- Vertex 3: (1, -2)
- Vertex 4: (4, -2)
To find the coordinates of a rectangle with a given vertex and dimensions, you'll need to consider the rectangle's position and orientation.
Given that the vertex is (1, 2) and the dimensions are 3 units by 4 units, we can determine the coordinates of the other three vertices.
1. Start with the given vertex (1, 2).
2. To find the second vertex, move 3 units horizontally from the given vertex since the rectangle is 3 units wide. In this case, add 3 to the x-coordinate. So, the second vertex is (1 + 3, 2), which simplifies to (4, 2).
3. To find the third vertex, move 4 units vertically from the given vertex since the rectangle is 4 units tall. In this case, add 4 to the y-coordinate. So, the third vertex is (1, 2 + 4), which simplifies to (1, 6).
4. The fourth vertex can be found by moving both horizontally and vertically from the given vertex. Adding 3 units horizontally and 4 units vertically, we get (1 + 3, 2 + 4), which simplifies to (4, 6).
Therefore, the coordinates of the rectangle with a vertex at (1, 2) and dimensions 3 units by 4 units are:
(1, 2), (4, 2), (1, 6), and (4, 6).