Question

A (-2, 4), C(4, 10) and D(-2, 10) are the vertices of a square ABCD. Use the graphical method to find the co-ordinates of the fourth vertex B. Also, find:
(i) The co-ordinates of the mid-point of BC;
(ii) The co-ordinates of the mid-point of CD and
(iii) The co-ordinates of the point of intersection of the diagonals of the square ABCD.

Answer 1

Given A(-2, 4), C(4,10) and D(-2,10) are the vertices of a square ABCD

After plotting the given points A(- 2, 4), C(4,10) and D(- 2,10) on a graph paper; joining D with A and D with C. Now complete the square ABCD
As is clear from the graph B(4, 4)
Now from the graph we can find the midpoints of the sides BC and CD the co-ordinates of the diagonals of the square.
Therefore the coordinates of the mid-point of BC is E(4, 7) and the coordinates of the mid-point of CD is F(1,10) and the coordinates of the diagonals of the square is G(1, 7).