A rectangle ABCD has three of its vertices at A(2, 1),
B(6, 1), and C(6, 3). Find the fourth vertex D and the
area of rectangle ABCD.
"college" geometry?
Why not just plot the 3 given points and then count to find what the 4th point has to be?
To find the fourth vertex D of the rectangle ABCD, we need to understand the properties of a rectangle.
A rectangle is a quadrilateral (a four-sided polygon) with opposite sides that are equal in length and all interior angles that are right angles (90 degrees).
Given the coordinates of vertices A, B, and C, we can use this information to find the fourth vertex D.
Since A(2, 1) and B(6, 1) have the same y-coordinate (1), we can conclude that side AB is horizontal. Therefore, the fourth vertex D should have the same y-coordinate since it is on the opposite side of the rectangle.
Now, since B(6, 1) and C(6, 3) have the same x-coordinate (6), we can conclude that side BC is vertical. Therefore, the fourth vertex D should have the same x-coordinate since it is on the opposite side of the rectangle.
So, the x-coordinate of D would be 2 (same as A), and the y-coordinate of D would be 3 (same as C). Therefore, the fourth vertex D is D(2, 3).
To find the area of rectangle ABCD, we can use the formula: Area = length × width.
Length = AB = 6 - 2 = 4 units
Width = BC = 3 - 1 = 2 units
Area = 4 × 2 = 8 square units.
Therefore, the fourth vertex D is D(2, 3) and the area of rectangle ABCD is 8 square units.