A rectangle has vertices at (6,2,), (6, -6,), (-1, 2). Write the coordinates of the fourth vertex and find the area and perimeter of the rectangle
(Please help, I'm really confused by these.)
(-1,-6)
The perimeter is 30
Area is 56
(6,2), (6,-6), (-1,2), ((-1,-6)).
P = 2(2-(-6)) + 2(6-(-1)) = 16 + 14 = 30 Units.
Area = L*W = (2-(-6)) * (6-(-1)) = 8 * 7 = 56 Sq. units.
To find the coordinates of the fourth vertex of the rectangle, we can use the fact that opposite sides of a rectangle are parallel and equal in length.
Let's call the given vertices as follows:
A = (6, 2)
B = (6, -6)
C = (-1, 2)
The fourth vertex will be D. To find its coordinates, we can use the fact that the line connecting A and C will be parallel to the line connecting B and D.
The x-coordinate of D will be the same as B, which is 6. The y-coordinate of D will be the same as C, which is 2. Therefore, the coordinates of D are (6, 2).
To find the area of the rectangle, we need to determine the lengths of its sides. We can do this by finding the distance between the given vertices.
The length of side AB is the difference in y-coordinates:
AB = |2 - (-6)| = 8
The length of side BC is the difference in x-coordinates:
BC = |-1 - 6| = 7
Since opposite sides of a rectangle are equal, the length of side CD will also be 8, and the length of side DA will be 7.
The area of a rectangle is given by the formula:
Area = width * height
In this case, the width is 7 and the height is 8, so the area of the rectangle is:
Area = 7 * 8 = 56 square units.
To find the perimeter of the rectangle, we can sum the lengths of all four sides:
Perimeter = AB + BC + CD + DA
Perimeter = 8 + 7 + 8 + 7 = 30 units.
Therefore, the coordinates of the fourth vertex are (6, 2), the area of the rectangle is 56 square units, and the perimeter of the rectangle is 30 units.