Question

If the points A(1,-2) B(2,3) C(a,2) and D(-4,-3) form a parallelogram find the value of a and height of a parallelogram taking AB as base

Answer 1

you should first find the midpoint of BD and then by mid point theorem of Section formula find out the value of a taking over the midpoint of AC which is equal to the midpoint of a d as the diagonals of a parallelogram bisect each other

Answer 2

Answer:

In Parallelogram ,

AB = CD Then, AB²=CD²

So,

AB²=[√(2-1)²+(3- {-2})²]² = (2-1)² + (3+2)² = 1+25=26

CD²=[√(-4-a)²+(-3-2)²]² = (4+a)² + (5)² = 16+a²+8a+25 = a²+8a+41

26 = a²+8a+41

a²+8a+15=0

a²+3a + 5a +15=0

a(a+3)+5(a+3)=0

(a+3)(a+5)=0

So, a= -3 or -5

You can find out its area by = ar(triangle ABC) + ar(triangle DBC)

And we know Ar of Parallelogram = Height x base(AB=26 units)

You will find Height