Question

In a parallelogram BEST,BE=12cm,ES=10cm, BT = (2x+2)cm and TS= (4+y)cm.

a) Draw the figure

b) Calculate the value of x and y

Answer 1

Answer:

Given three vertices of a parallelogram ABCD are A(3,−1,2),B(1,2,−4) and C(−1,1,2) .

Let the coordinates of the fourth vertex be D(x,y,z).

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

Therefore in parallelogram ABCD, AC and BD bisect each other .

∴ Mid-point of AC= Mid-point of BD

⇒(

2

3−1

,

2

−1+1

,

2

2+2

)=(

2

x+1

,

2

y+2

,

2

z−4

)

⇒(1,0,2)=(

2

x+1

,

2

y+2

,

2

z−4

)

⇒

2

x+1

=1,

2

y+2

=0 and

2

z−4

=2

⇒x=1,y=−2 and z=8

Thus, the coordinates of the fourth vertex are (1,−2,8)

Step-by-step explanation:

hope it's help u