Question

abcd is a parallelogram where a(x y) b(5 8) c(4 7) and d(2 -4). find the coordinates of a​

Answer 1

Step-by-step explanation:

Here,

ABCD is a parallelogram where A(x,y), B(5,8), C(4,7) and D(2,-4) are the vertices of a parallelogram.

Then,

AB = CD

Using distance formula,

√(x-5)²+(y-8)² = √(4-2)²+(7+4)²

or, (x-5)²+(y-8)² = 2² + 13²

Equating on both sides

(x-5)²=2² And, (y-8)²=13²

or, x-5=2 or, y-8=13

or, x=5+2 or, y=13+8

i.e. x=7 i.e. y= 21

Hence,

x=7 and y=21

Answer 2

Question -

ABCD is a parallelogram where A(x, y) , B(5,8), C(4,7) and D(2,-4), find the coordinates of A

Solution -

In parallelogram ABCD, A(x, y) , B(5,8), C(4,7) and D(2,-4).

The diagonals of a parallelogram bisect each other.

O is the point of intersection of AC and BD

Therefore, O is the midpoint of BD, its

coordinates

$= ( \frac{2 + 5}{2} , \frac{ - 4 + 8}{2} )$

$= ( \frac{7}{2},2)$

Since, O is also the midpoint of AC,

$\implies \frac{x + 4}{2} = \frac{7}{2}$

By cross multiplying,

$\implies \: 2(x + 4) = 7 \times 2$

$\implies \: 2x + 8 = 14$

$\implies \: 2x = 14 - 8$

$\implies \: 2x = 6$

$\implies \: x = \frac{6}{2}$

$\implies \: x = 3$

And,

$\implies \: \frac{y + 7}{2} = 2$

By cross multiplying,

$\implies \: y + 7 = 2 \times 2$

$\implies \: y + 7 = 4$

$\implies \: y = 4 - 7$

$\implies \: y = - 3$

Therefore the coordinates of A is (3,-3)