Question

If A(1, 3); B(-1, 2); C(x, 4) and D(2, 5) are vertices of parallelogram then write the value of x.​

Answer 1

Answer:

x=0

Step-by-step explanation:

DRAW [] ABCD

Use diagonal BD and centre O

Since,diagonals of ||gm bisect each other

Therefore,By midpoint formula

x(O)= x(D)+x(B)/2

x(O)=2+(-1)/2

""x(O)=1/2""

Similarly,

y(O)=y(D)+y(B)/2

y(O)=5+2/2

""y(O)=7/2""

(x,y)O=1/2,7/2

Now,diagonal AC and co ordinates of O

By midpoint formula

x(O)=x(C)+x(A)/2

1/2=x+1/2

x+1=2/2

x+1=1

x=1-1

x=0

LETS CHECK

BY DISTANCE FORMULA

(1+1)^2+(3-2)^2=(2-0)^2+(5-4)^2

4+1=4+1

5=5

AB=BC

HOPE IT HELPS