Question

points A(3,1),B(5,1),C(a,b) and D(4,3) are the vertices of a parallelogram ABCD.Find the values of a and b

Answer 1

WE THE DIAGONAL IN A PARALLELOGRAM BISECTS EACH OTHER SO
AC=BD
(3+a/2, 1+b/2) =(5+4/2, 1+3/2)
3+a/2=9/2 , 1+b/2=4/2
3+a=9 1+b=4
a=6 b=3



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Answer 2

Answer:

The values of a and b are 6 and 3

Step-by-step explanation:

Given the points A(3,1),B(5,1),C(a,b) and D(4,3) are the vertices of a parallelogram ABCD.

we have to find the values of a and b.

By mid-point formula

If $(x_1,y_1)$ and $(x_2,y_2)$ are the points of end-points of joining the line-segment then the coordinates of mid-point are

$(\frac{x_1+x_2}{2},\frac{y_1+y_2}{+2})$

As the diagonals of parallelogram bisect each other

⇒ $(\frac{3+a}{2},\frac{1+b}{2})=(\frac{5+4}{2},\frac{1+3}{2})$

⇒ $(\frac{3+a}{2},\frac{1+b}{2})=(\frac{9}{2},2)$

Comparing both sides

$\frac{3+a}{2}=\frac{9}{2}$

$3+a=9$ ⇒ $a=6$

$\frac{1+b}{2}=2$

$1+b=4$ ⇒ $b=3$

The values of a and b are 6 and 3