Question

The vertices of a rectangle ABCD are A (-1,0) B ( 2,0) C ( a , b ) D (-1,4) then length of the diagonal AC

Answer 1

Answer:

The diagonal AC is of length = 5.

Step-by-step explanation:

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  = $\sqrt{(2 - (-1))^2 + (4 -0)^2} = \sqrt{9 + 16} = \sqrt{25} = 5$.