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.)
SKETCH IT !
last corner at x = -1, y = -6
top goes from -1 to +6 (how long?)
side goes from -6 to +2 (how long?)
See previous post: Thu, 10-5-17, 6:32 PM.
To find the fourth vertex of the rectangle, we can use the fact that opposite sides of a rectangle are parallel.
Since the given vertices are at (6, 2), (6, -6), and (-1, 2), we can see that the top and bottom sides of the rectangle are horizontal. This means that the fourth vertex should also have the same y-coordinate as the first vertex, which is 2.
Similarly, the left and right sides of the rectangle are vertical, so the fourth vertex should have the same x-coordinate as the second vertex, which is 6.
Therefore, the coordinates of the fourth vertex are (6, 2).
To find the area of the rectangle, we can use the formula: Area = length * width.
To calculate the length, we can find the difference in the x-coordinates of the first and second vertices: length = 6 - (-1) = 7.
To calculate the width, we can find the difference in the y-coordinates of the first and third vertices: width = 2 - (-6) = 8.
Thus, the area is: 7 * 8 = 56 square units.
To find the perimeter of the rectangle, we can use the formula: Perimeter = 2 * (length + width).
In this case, the length is 7 and the width is 8, so the perimeter is: 2 * (7 + 8) = 2 * 15 = 30 units.
Therefore, the coordinates of the fourth vertex are (6, 2), the area of the rectangle is 56 square units, and the perimeter is 30 units.