Question

The vertices of a parallelogram taken in order are A(3, 4), B(9, 5), C(7, 2x), and D(y, 15). Find the value of xy.​

Answer 1

Answer:

x = 20 and y = 14 plz mark me a brainest

Answer 2

Given:

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

To find:

Find the value of xy.​

Solution:

From given, we have,

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]

By equating the equal coordinates, we get,

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

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

y =1 and x = 8.

The value of xy is 8