Q= if A(-2,1),B(a,0),C(4,b),D(1,2) are the vertices of a parallelogram ABC, find the values of a and b. Hence find the length of its sides
Answers
Answered by
30
Midpoint of AC = Midpoint of BD
=> ( 4-2/2 , b+1/2) = (a+1/2 , 0+2/2)
=> ( 1 , b+1/2) = (a+1/2 , 1)
=> a+1/2 = 1 and b+1/2 = 1
=> a + 1 = 2 and b + 1 = 2
=> a = 1 and b =1
=> ( 4-2/2 , b+1/2) = (a+1/2 , 0+2/2)
=> ( 1 , b+1/2) = (a+1/2 , 1)
=> a+1/2 = 1 and b+1/2 = 1
=> a + 1 = 2 and b + 1 = 2
=> a = 1 and b =1
Answered by
2
Answer:
a = 1, b = 1, AB = √10, BC = √10
Step-by-step explanation:
As we know the diagonals of a parallelogram bisect each other, we can take their midpoints.
Midpoint of diagonal AC = Midpoint of diagonal BD.
Given A(-2,1),B(a,0),C(4,b),D(1,2).
By using the formula (x1 + x2)/2 and (y1 + y2)/2 we have
(-2 + 4)/2, (1 + b)/2 = (a + 1)/2 , (0 + 2)/2
on simplifying we get (b+1)/2 = 1 and (a+1)/2 = 1
So a = 1 and b = 1
Using the distance formula the length of parallelogram can be obtained.
AB = √(x2 - x1)^2 + (y2 - y1)^2
= √(1 -(- 2)^2 + (0 -1)^2
= √9 -1
AB = √10
BC = √(4 - 1)^2 + (1 - 0)^2
BC = √10
It is a rhombus since the sides are equal.
Similar questions