Question

The points A (2, -2), B (8,4) and C (5,7) are three vertices of rectangle ABCD. Plot these points on a graph

paper and hence, find the coordinate of its fourth vertex D​

Answer 1

Solution:-

➡️Let (a,b) be the required vertex D.

➡️In any parallelogram the diagonals AC and BD bisect each other.That is the midpoint of the diagonal AC will be equal to the

midpoint of the diagonal BD

➡️Midpoint of the diagonal AC = (x1+x2)/2 , (y1+y2)/2

                                 A(2,-2) C(5,7)

                    x1 = 2, x2 = 5 ,y1 = -2 and y2 = 7

                                    = (2 + 5)/2 , (-2+7)/2

                                    = 7/2 ,5/2

➡️Midpoint of the diagonal BD =  (x1+x2)/2 , (y1+y2)/2

                               B(8,4) D(a,b)

                   x1 = 8,x2 = a, y1 = 4 and y2= b

                               = (8 + a)/2 , (-4+b)/2

➡️midpoint of the diagonal AC = midpoint of the diagonal BD

                       (7/2,5/2) =  (8+a)/2,(-4+b)/2

                 (8+a)/2 =  7/2                (-4+b)/2 = 5/2

                      8+a = 7                      -4 + b = 5

                         a = 7-8                         b = 5 + 4

                         a = -1                           b = 9

➡️So the required vertex is (-1,9)

Answer 2

Answer:

(-1, 1)

Step-by-step explanation: