Given the rectangle ABCD on the coordinate plane. A=(0,0) B=(4,-4) C=(7,-1) D=(3,3)
(3 points)
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The length of side AB in simplest radical form is Response area.
The length of side BC in simplest radical form is Response area.
The area of rectangle ABCD in simplest radical form is Response area.
To find the length of side AB, we can use the distance formula. The distance formula is given by:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Using the coordinates of points A and B, we have:
x1 = 0, y1 = 0 (coordinates of point A)
x2 = 4, y2 = -4 (coordinates of point B)
Distance AB = √((4 - 0)^2 + (-4 - 0)^2)
= √(4^2 + (-4)^2)
= √(16 + 16)
= √32
Therefore, the length of side AB in simplest radical form is 4√2.
To find the length of side BC, we can use the same distance formula. Using the coordinates of points B and C, we have:
x1 = 4, y1 = -4 (coordinates of point B)
x2 = 7, y2 = -1 (coordinates of point C)
Distance BC = √((7 - 4)^2 + (-1 - (-4))^2)
= √(3^2 + 3^2)
= √(9 + 9)
= √18
Therefore, the length of side BC in simplest radical form is 3√2.
To find the area of rectangle ABCD, we can use the formula:
Area = length * width
Since side AB and side BC are two adjacent sides of the rectangle and perpendicular to each other, the area can be found as the product of their lengths.
Area = AB * BC
= (4√2) * (3√2)
= (4 * 3) * (√2 * √2)
= 12 * 2
= 24
Therefore, the area of rectangle ABCD in simplest radical form is 24.