Question

the three vertices of a parallelogram are 3, 4 and 3, 8 and 9, and find the fourth vertex

Answer 1

Question : The three vertices of a parallelogram are (3,4) ,(3,8) and (9,8). Find the fourth vertex.

Answer :

Given :

Let ABCD be a parallelogram.

then

A ( 3,4),

B (3,8)

C (9,8 ).

Let the coordinates of D = (x,y)

we know that the diagonals of a parallelogram bisect each other.

Coordinates of the mid-point of AC = Coordinates of the mid-point of BD

LHS = RHS

3+9/2 , 4+8/2 = 3+x/2 , 8+y/2

12/2 , 12/2     = 3+x/2 , 8+y/2

6 = 3+x/2     = 6 =  8+y/2

12 = 3+x      = 12 = 8+y

12-3 = x   , = 12-8 = y

 9 =x               = 4 = y

∴ Coordinates of the fourth vertex are ( 9, 4)

Parallelogram :

• It is a quadrilateral with two pairs of parallel sides.
• Opposite sides are parallel .
• Opposite sides are congruent.
• To find the area of a parallelogram, multiply the base by the height.
• The diagonals of a parallelogram bisect each other.
• It has two pairs of equal opposite angles.