The three vertices of a parallelogram are (3, 4), (3, 8) and (9, 8). Find the fourth vertex.
Answers
Answered by
3
(9,4)
Step-by-step explanation:
Mid point of BD=
Mid point of AC=
Answered by
2
Coordinates of fourth vertex are (9,4)
•Since, diagonals of parallelogram
bisects each other.
AO = OC
BO = OD
•let coordinates of O be (h,k)
•By section formula
•As, AO = OC
h = (m2x1 +m1x2)/(m1+m2)
h = [(1)(3)+(1)(9)](1+1)
h = (3+9)/2
h = 12/2
h = 6
k = (m2Y1 +m1Y2)/(m1+m2)
k = [(1)(4)+(1)(8)](1+1)
k = (4+8)/2
k = 12/2
k = 6
coordinates of O are (6,6)
•Now, BO = OD
•let coordinates of D be (x,y)
•By section formula
6 = (m2x1 +m1x2)/(m1+m2)
6 = [(1)(3)+(1)(x)](1+1)
6 = (3+x)/2
12 = 3+x
x = 9
6 = (m2Y1 +m1Y2)/(m1+m2)
6 = [(1)(8)+(1)(y)](1+1)
6 = (8+y)/2
12 = 8+y
y = 4
•coordinates of D are (9,4)
Attachments:
Similar questions