Question

ifa(-2 1) b(-4 -5) c(4 b) d(1 2) are the vertices of a parallelogram ABCD find the values of a and b hence find lengths of its sides

Answer 1

We know that diagonals of a parallelogram bisect each other.

Coordinates of the midpoint of AC = coordinates of the midpoint of BD

Midpoint of AC = Midpoint of BD

(4-2/2, b+1/2) = (a+1/2, 0+2/2)
(2/2, b+1/2) = (a+1/2, 2/2)
(1, b+1/2) = (a+1/2, 1)

so,

1 = a+1/2
2 = a+1
∴,a = 1

and

b+1/2 = 1
b+1=2
∴,b = 1

Therefore, the coordinates are A(-2,1), B(1,0), C(4,1) and D(1,2).

AB=DC=√(1+2)² + (0-1)² = √9+1 = √10units
AD=BC=√(1+2)² + (2-1)² = √9+1 = √10units

MARK BRAINLIEST!