Question

In square ABCD; A = (3, 4), B = (-2, 4) and C = (-2, -1). By plotting these points on a graph paper, find the co-ordinates of vertex D. Also, find the area of the square.

Answer 1

Given that in square ABCD ; A(3,4), B(-2,4) and C(-2,-1)

After plotting the given points A(3,4), B(-2,4) and C(-2,-1) on a graph paper; joining B with C and B with A. From the graph it is clear that the vertical distance between the points B(-2,4) and C(-2,-1) is 5 units and the horizontal distance between the points B(-2,4) and A(3,4) is 5 units, therefore the vertical distance between the points A(3,4) and D must be 5 units and the horizontal distance between the points C(-2,-1) and D must be 5 units. Now complete the square ABCD
As is clear from the graph D(3,-1)
Now the area of the square ABCD is given by area of ABCD = (side)² = (5)² = 25 units