geometry- On the coordinate plane, draw a rectangle ABCD with vertices at A (1,4), B(5,4), C(5,1) and D (1,1). Then graph and describe the new rectangle formed when you subtact 3 from each coordinate of the vertices in rectangle ABCD.
Can't graph, but the new rectangle is just the old rectangle shifted left 3 and down 3.
Well, when you subtract 3 from each coordinate of the vertices in rectangle ABCD, we can call the new rectangle EFGH. So, let's see...
The coordinates of vertex A=(-2,1), the coordinates of vertex B=(2,1), the coordinates of vertex C=(2,-2), and the coordinates of vertex D=(-2,-2).
Now, let's plot these points on the coordinate plane and see what the new rectangle EFGH looks like:
E (-2,1) F (2,1)
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H (-2,-2) G (2,-2)
And there you have it! The new rectangle EFGH is formed by subtracting 3 from each coordinate of the vertices in rectangle ABCD. Voila!
To graph the rectangle ABCD with vertices at A(1,4), B(5,4), C(5,1), and D(1,1) on the coordinate plane, follow these steps:
1. Draw a set of axes with x-axis and y-axis intersecting at the origin (0,0).
2. Locate point A at coordinates (1,4). Plot a point on the graph at (1,4).
3. Locate point B at coordinates (5,4). Plot a point on the graph at (5,4).
4. Locate point C at coordinates (5,1). Plot a point on the graph at (5,1).
5. Locate point D at coordinates (1,1). Plot a point on the graph at (1,1).
6. Connect the points A, B, C, and D to form a rectangle.
Now, to find the new coordinates by subtracting 3 from each coordinate of the vertices of rectangle ABCD, follow these steps:
1. Subtract 3 from the x-coordinate of point A: (1 - 3, 4 - 3) = (-2, 1).
2. Subtract 3 from the x-coordinate of point B: (5 - 3, 4 - 3) = (2, 1).
3. Subtract 3 from the x-coordinate of point C: (5 - 3, 1 - 3) = (2, -2).
4. Subtract 3 from the x-coordinate of point D: (1 - 3, 1 - 3) = (-2, -2).
Therefore, the new rectangle formed by subtracting 3 from each coordinate of the vertices in rectangle ABCD has vertices at A'(-2,1), B'(2,1), C'(2,-2), and D'(-2,-2).
To draw the original rectangle ABCD on the coordinate plane, we use the given coordinates for each vertex:
A (1, 4)
B (5, 4)
C (5, 1)
D (1, 1)
Now, to subtract 3 from each coordinate of the vertices in rectangle ABCD, we subtract 3 from the x-coordinate and the y-coordinate of each point. Let's calculate the new coordinates:
A' = (1 - 3, 4 - 3) = (-2, 1)
B' = (5 - 3, 4 - 3) = (2, 1)
C' = (5 - 3, 1 - 3) = (2, -2)
D' = (1 - 3, 1 - 3) = (-2, -2)
Now, let's graph and describe the new rectangle formed by connecting the vertices A', B', C', and D':
A' (-2, 1) is the bottom left corner of the new rectangle.
B' (2, 1) is the bottom right corner of the new rectangle.
C' (2, -2) is the top right corner of the new rectangle.
D' (-2, -2) is the top left corner of the new rectangle.
Connecting the vertices A', B', C', and D' on the coordinate plane, we have a new rectangle with sides parallel to the original rectangle ABCD.
The new rectangle is located in the fourth quadrant (-x, -y). It has a width of 4 units (from A' to B') and a height of 3 units (from A' to D'). The side lengths are equal to the original rectangle ABCD but shifted by 3 units in the negative x and y directions.