Question

if the points A (6, 1)B(8, 2)c(9, 4) and d(x, y )are the vertices of a parallelogram taken in order then find the value of x and y​

Answer 1

Answer:

x = 6+9-8

x = 7

y = 1+4-2

y = 3

the coordinates (x,y) = (7,3)

Answer 2

The values of x and y are 7 and 3.

Step-by-step explanation:

Given, A(6, 1), B(8, 2), C(9, 4) and D(x, y ) be vertices of a parallelogram ABCD.

To find, the values of x and y = ?

We know that,

The diagonals of a parallelogram bisect each other.

Midpoint of AC = Midpoint of BD

Midpoint of AC = $(\dfrac{6+9}{2}, \dfrac{1+4}{2})$

=$(\dfrac{15}{2}, \dfrac{5}{2})$

Midpoint of AC = $(\dfrac{8+x}{2}, \dfrac{2+y}{2})$

∴ $\dfrac{15}{2}=\dfrac{8+x}{2}$

⇒ 8 + x = 15

⇒ x = 15 - 8 = 7

Also, $\dfrac{5}{2}=\dfrac{2+y}{2}$

⇒ 2 + y = 5

⇒ y = 5 - 2 = 3

Thus, the values of x and y are 7 and 3.