Question

If P (a,11), Q (5,b),R (2,15) and S (1,1) from a parallelogram . Find a and b. Also find area of PORS. only fast brainlist answer this

Answer 1

The parallelogram PQRS is:



One of the properties of a parallelogram states that:

The Diagonals of a parallelogram bisect each other.

So, joining the diagonals of the Parallelogram,



The intersection of the diagonals is O(x,y).

=> Taking diagonal PR to find co-ordinates of O:

P(a,−11)=(x1,y1)P(a,−11)=(x1,y1)

R(2,15)=(x2,y2)R(2,15)=(x2,y2)

O(x,yO(x,y))

Applying Mid-Point Formula,

O(x,y)=[(x1+x2)÷2,(y1+y2)÷2]O(x,y)=[(x1+x2)÷2,(y1+y2)÷2]

O(x,y)=[(a+2)÷2,(−11+15)÷2]O(x,y)=[(a+2)÷2,(−11+15)÷2]

O(x,y)=((a+2)÷2,2)O(x,y)=((a+2)÷2,2) ……… (1)

=> Taking diagonal QS to find co-ordinates of O:

Q(5,b)=(x1,y1)Q(5,b)=(x1,y1)

S(1,1)=(x2,y2)S(1,1)=(x2,y2)

O(x,y)=((a+2)÷2,2)O(x,y)=((a+2)÷2,2) from, (1)

Applying Mid-Point Formula,

O(x,y)=[(x1+x2)÷2,(y1+y2)÷2]O(x,y)=[(x1+x2)÷2,(y1+y2)÷2]

((a+2)÷2,2)((a+2)÷2,2)=[(5+1)÷2,(b+1)÷2]=[(5+1)÷2,(b+1)÷2]

((a+2)÷2,2)=(3,(b+1)÷2)((a+2)÷2,2)=(3,(b+1)÷2)

Therefore, from the above equation,

(a+2)÷2=3(a+2)÷2=3

a=6–2a=6–2

a=4a=4

(b+1)÷2=2(b+1)÷2=2

b=4–1b=4–1

b=3b=3

Therefore, values of a and b are 4 and 3.

Answer 2

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