Question

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

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

The values of a and b are 6 and 3

Step-by-step explanation:

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

we have to find the value of a and b

As the diagonals of parallelogram bisect each other i.e the mid-points of diagonals AC and BD bisect each other.

By mid-point formula,

The coordinates of of mid-point of line segment joining the points (a,b) and (c,d) are $(\frac{a+c}{2}, \frac{b+d}{2})$

Mid point of AC=Mid-point of BD

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

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

Comparing both sides

$\frac{3+a}{2}=\frac{9}{2}$  and  $\frac{1+b}{2}=2$

⇒  3+a=9 and 1+b=4

⇒  a=6 and  b=3

The coordinate of point C is (6,3)