The vertices of a rectangle ABCD are A (-1, 0) B(2, 0) C(a, b) D(-1, 4)
The points A and B have the same y -coordinate that is y = 0, so the side AB is on the x-axis and is of length (2 - (-1)) = 3.
The point A and D have the same x co-ordinate that ix x = -1 , therefore side AD is parallel to the y axis and the length is (4 - 0) = 4.
The above two statements lead us to believe that CD is parallel to the x-axis and BC is parallel to the y -axis and that (a, b) is equal to (2, 4).
The co-ordinates form a rectangle given by the points A(-1, 0), B(2, 0), C(2, 4) and D (-1, 4).
The diagonal AC length is \(=\sqrt {(1-(-1))^2 + (4-0)^2}\)
\(=\sqrt {9 +16}\)
\(=\sqrt {25}\)
\(=5\).
