Question

Plot the points A(1,0),B(4,0) and C(4,4) Find the coordinates of the point D such that ABCD is a rectangle

Answer 1

Given: A(1,0),B(4,0) and C(4,4).

To find:  Coordinates of the point D such that ABCD is a rectangle.

Solution:

• Now, we have given three coordinates, So first we need to find the mid point of AC to find the point D. Let the point D be (x,y) and the centre of diagonal be O.
• So using mid point formula: (x1 + x2/2, y1 + y2/2)

              O = ( (4+1) / 2, (4+0) / 2 )

              O = ( 5/2 , 2 )

• Similarly, using mid point, we can find D:

              ( 5/2 , 2 ) = ( 4+x / 2, y+0 /2 )

• Equating the coordinates, we get:

              4+x / 2 = 5/2, y+0 / 2 = 2

• Now solving for x and y, we get:

              4+x = 5, y = 4

              x = 1,  y = 4

Answer:

              The coordinates of the point D such that ABCD is a rectangle is x = 1,  y = 4.