Question

point A(3,1), B(5,1) c(a,b) and D(4,3) are vertex of parallelogram ABCD. find the value of a b​

Answer 1

Answer:

C(6,3)

a=6 and b=3

Step-by-step explanation:

Point A(3,1), B(5,1) c(a,b) and D(4,3) are vertex of parallelogram.  

Please see the attachment for figure.

The diagonals of parallelogram are intersect at a mid point of diagonals.  

We can say mid point of BD is equivalent to mid point of AC.  

Formula, Using mid point formula

$(x,y)\rightarrow (\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}$

Mid point of BD at O

$O(x,y)=(\dfrac{5+4}{2},\dfrac{1+3}{2})\Rightarrow (4.5,2)$

Mid point of AC at O  

$O(x,y)=(\dfrac{3+a}{2},\dfrac{1+b}{2})$

$O(x,y)=(\dfrac{3+a}{2},\dfrac{1+b}{2})=(4.5,2)$

$\dfrac{3+a}{2}=4.5\Rightarrow a=6$

$\dfrac{1+b}{2}=2\Rightarrow b=3$

Hence, The value of a and b are 6 and 3 respectively. C(6,3)

Answer 2

Answer:

Point C = (6,3)

Step-by-step explanation:

point A(3,1), B(5,1) c(a,b) and D(4,3) are vertex of parallelogram ABCD. find the value of a b​

ABCD is a parallelogram so

AB ║ CD and AB = CD

Slope of AB = Slope of CD

slope of AB = m

m = (by - ay)/(bx - ax)

=> m = (1-1)/(5-3)

=> m = 0/2

=> m = 0

Slope of CD = 0

so equation of line CD

y = 0 * x + c

Point D = (4, 3)

so 3 = 0*4 + c

=> c = 3

equation of line CD = y = 3

Let say Point C ( Cx , Cy)

Cy = 0 * Cx + 3 = 3

length of AB² = (5-3)² + (1-1)² = 2²

Legth of CD² = (Cx - 4)² + (3-3)² = (Cx-4)²

=> (Cx-4)² = 2²

=> Cx - 4 = 2

=> Cx = 6

Point C = (6,3)