You are graphing rectangle ABCDA, B, C, D in the coordinate plane. The following are three of the vertices of the rectangle:
A =(−7,−7.5), B = (−3,7.5), C = (−3,2.5)
What are the coordinates of point D?
To find the coordinates of point D, we need to use the fact that a rectangle has parallel sides, so the vector from B to C is perpendicular to the vector from C to D. We can use this idea to find the coordinates of D as follows:
1. Find the vector from B to C:
BC = (−3,7.5) − (−3,2.5) = (0,5)
2. Find a vector perpendicular to BC:
One way to do this is to swap the components of BC and negate one of them, like so:
BC' = (5,0) or (−5,0)
Either of these vectors is perpendicular to BC.
3. Add the vector BC' to point A to get point D:
AD = BC'
D = A + AD = (−7,−7.5) + (−5,0) = (−12,−7.5)
Therefore, the coordinates of point D are (−12,−7.5).
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ABCDA, B, C, D is graphed in the coordinate plane. The following are the vertices of the rectangle:
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A(2,0)A, left parenthesis, 2, comma, 0, right parenthesis,
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6
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B(6,0)B, left parenthesis, 6, comma, 0, right parenthesis,
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6
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7
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C(6,7)C, left parenthesis, 6, comma, 7, right parenthesis, and
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2
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D(2,7)D, left parenthesis, 2, comma, 7, right parenthesis.
What is the area of rectangle
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ABCDA, B, C, D?
To find the area of rectangle ABCDA, we first need to find the length and width of the rectangle. We know that side AB has length 6 - 2 = 4, and side AD has length 7 - 0 = 7. Therefore, the length and width of the rectangle are 7 and 4, respectively.
The area of a rectangle is calculated by multiplying the length by the width, so we have:
Area = Length × Width = 7 × 4 = 28
Therefore, the area of rectangle ABCDA is 28 square units.
Rectangle
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ABCDA, B, C, D is graphed in the coordinate plane. The following are the vertices of the rectangle:
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A(−7,−5),B(−7,6),A, left parenthesis, minus, 7, comma, minus, 5, right parenthesis, comma, B, left parenthesis, minus, 7, comma, 6, right parenthesis, comma
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4
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C(−4,6)C, left parenthesis, minus, 4, comma, 6, right parenthesis, and
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4
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D(−4,−5)D, left parenthesis, minus, 4, comma, minus, 5, right parenthesis.
Given these coordinates, what is the length of side
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CDC, D of this rectangle?
To find the length of side CD, we first need to find the coordinates of points C and D. We can see that the y-coordinates of both C and D are 6 and -5, respectively, so we just need to focus on the x-coordinates. We have:
Point C: x = -4
Point D: x = -7
Therefore, the length of side CD is the difference between these x-coordinates:
CD = (-4) - (-7) = 3
So the length of side CD is 3 units.
You are graphing rectangle ABCDA, B, C, D in the coordinate plane. The following are three of the vertices of the rectangle:
A = (3,5), B = (3,−4),, C = (−2,−4)C,
What are the coordinates of point D?
To find the coordinates of point D, we need to understand the properties of a rectangle. In a rectangle, opposite sides are parallel and equal in length. This means that the segments AB and CD are parallel and equal in length, as well as the segments BC and AD.
To find the coordinates of point D, we can use the following steps:
1. Find the length of segment AB. Use the distance formula, which is √((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) and (x2, y2) are the coordinates of two points. In this case, the coordinates of A are (-7, -7.5) and the coordinates of B are (-3, 7.5). Plugging these values into the distance formula, we get AB = √((-3 - (-7))^2 + (7.5 - (-7.5))^2) = √((-3 + 7)^2 + (7.5 + 7.5)^2) = √(4^2 + 15^2) = √(16 + 225) = √241.
2. Since AB and CD are parallel and equal, we can use the length of AB to find the coordinates of point D. Start from point C and move in the opposite direction of AB. Since the x-coordinate of C is -3, we subtract the length of AB from -3 to find the x-coordinate of point D. Therefore, the x-coordinate of D is -3 - √241.
3. To find the y-coordinate of point D, we can use the y-coordinate of C, which is 2.5. Since AD and BC are parallel and equal, the y-coordinate of D will be the same as the y-coordinate of C. Therefore, the y-coordinate of D is 2.5.
So, the coordinates of point D are (-3 - √241, 2.5).