if the points A (-4,-2) B(3,-5) C(3,2) and D(2,a)form a parallelogram,find the value of "a" and the height of the - Maths -

Question

if the points A (-4,-2) B(3,-5) C(3,2) and D(2,a)form a
parallelogram,find the value of "a" and the height of the
parallelogram taking ABas base

Priyanka Kedia · Accepted Answer

Since opposite sides of a parallelogram are equal Therefore,
AB=CD⇒AB2=CD2 Using distance formula between two points;
d=x2-x12+y2-y12⇒3+42+-5+22=2-32+a-22⇒49+9=1+a-22⇒a-22=57⇒a-2=±57⇒a=2±57
Area of ∆ having coordinates x1,y1; x2,y2 ; x3,y3 is given
by,area = 12x1y2-y3 + x2y3-y1 + x3y1 - y2Area of ||gm
ABCD=2×Area of ΔABC
=2×124×-5+3×2+3×-2-3×-2+3×-5+4×2
=-20+6-6--6-15+8 =-20+13 =7 square unitNow,Area of ||gm ABCD=Height
of ||gmh×Base AB⇒Height of ||gmh=Area of ||gm ABCDBase
AB =73+42+-5+22 =749+9 =758 unit
Hence, Height of ||gmh is 758 unit

if the points A (-4,-2) B(3,-5) C(3,2) and D(2,a)form a parallelogram,find the value of "a" and the height of the parallelogram taking ABas base