Question

the vertices of a parallelogram taken in order of A(3,4),b(9,5),c (7,2X) and d(y,15)
find the value of xy​

Answer 1

Step-by-step explanation:

If A(3,4), B(9,5), C(7,2X) and D(y,15) are the vertices of a parallelogram, then the diagonals intersect each other at a point.

So,

Mid-point of AC= Mid-point of BD.

Mid-point of a line joining (x1,y1) and (x2,y2):

p(x,y)=[x1+x2/2, y1+y2/2].

[3+7/2, 4+2x/2]=[9+y/2,5+15/2]

[10/2,4+2x/2]=[9+y/2, 20/2]

[5,4+2x/2]=[9+y/2,10]

By equating the equal coordinates:

5=9+y/2. 4+2x/2=10

10-9=y. 2x=20-4=16

1=y. x=16/2=8.

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Answer 2

Given:

The vertices of a parallelogram are A(3,4), B(9,5), C(7,2x) and D(y,15).

To find:

Values of x and y.

Solution:

The diagonals of a parallelogram intersect each other.

So,

Midpoint of AC = Midpoint of BD

Midpoint of a line joining two points $(x_1, y_1) and (x_2,y_2) =\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)$.

Midpoint of AC = $(\frac{7+3}{2} ,\frac{4+2x}{2} )$

Midpoint of BD = $(\frac{9+y}{2},\frac{5+15}{2})$

$\therefore (\frac{7+3}{2} ,\frac{4+2x}{2} )=(\frac{9+y}{2},\frac{5+15}{2})\\\\ On equating x and y, we get:\\(x,y) = (8,1).$

Therefore, the values of x and y are 8 and 1 respectively.