Question

Q7. The fourth D of a parallelogram
ABCD whose three vertices are
A(6,7), B(8,3) and C(0,-1) is​

Answer 1

Answer:

(8,3)is a correct answer because it is a correct answer

Answer 2

Solution :-

Let :-

The coordinates of the fourth vertex D = ( a , b )

We know :-

The diagonals of a parallelogram bisects each other.

That is :-

Midpoint of AC = Midpoint of BD

$\boxed{\bf Midpoint \ formula = \left( \dfrac{x_1+x_2}{2} \ , \ \dfrac{y_1+y_2}{2} \right) }$

Midpoint of AC :-

$\longrightarrow \sf \left( \dfrac{6+0}{2} \ , \ \dfrac{7+-1}{2} \right) \\\\\longrightarrow \left( \dfrac{6}{2} \ , \ \dfrac{6}{2} \right) \\\\\longrightarrow ( 3 \ , \ 3)$

Midpoint of BD :-

$\longrightarrow \sf \left( \dfrac{8+a}{2} \ , \ \dfrac{3+b}{2} \right)$

$\longrightarrow \sf \dfrac{8+a}{2} = 3 \\\\\longrightarrow 8+a = 6 \\\\\longrightarrow \bf a = -2$

$\longrightarrow \sf \dfrac{3+b}{2} = 3\\\\\longrightarrow 3+b = 6 \\\\\longrightarrow \bf b = 3$

Coordinates of D = ( -2 , 3 )