Question

lf ABCD is a parallelogram and B (4,7) C (5,1) and D (10,-5) find the coordinates of А.​

Answer 1

Step-by-step explanation:

Given :-

ABCD is a parallelogram and B (4,7), C (5,1) and D (10,-5).

To find :-

Find the coordinates of А?

Solution :-

Given that

ABCD is a Parallelogram.

Given vertices of ABCD are and B (4,7), C (5,1) and D (10,-5).

Let the coordinates of the point A be (x,y)

We know that

In Parallelogram,the diagonals bisect to each other.

=> Mid point of AC = Mid point of BD

The coordinates of the mid point of the linesegment joining points (x1, y1) and (x2, y2) is

( (x1+x2)/2 , (y1+y2)/2 )

Finding the midpoint of AC :-

Let (x1,y1) = A(x, y) => x1 = x and y1 = y

Let (x2, y2) = C(5,1) => x2 = 5 and y2 = 1

Mid point of AC = ( (x+5)/2 , (y+1)/2 ) ------(1)

Finding the midpoint of BD :-

Let (x1,y1) = B(4,7) => x1 = 4 and y1 = 7

Let (x2, y2) = D(10,-5) => x2 = 10 and y2 = -5

Mid point of BD = ( (4+10)/2 , (7+(-5))/2 )

=> ( 14/2 , (7-5)/2 )

=> ( 7,2/2 )

=> (7,1) ------(2)

We have ,

(1) = (2)

=> ( (x+5)/2 , (y+1)/2 ) = (7,1)

=> (x+5)/2 = 7 and (y+1)/2 = 1

=> x+5 = 7×2 and y+1 = 1×2

=> x+5 = 14 and y+1 = 2

=> x = 14-5 and y = 2-1

=> x = 9 and y = 1

Therefore, (x,y) = (9,1)

Answer:-

The coordinates of the point A is (9,1)

Used formulae:-

The coordinates of the mid point of the linesegment joining points (x1, y1) and (x2, y2) is

( (x1+x2)/2 , (y1+y2)/2 )

→ In Parallelogram,the diagonals bisect to each other.

Answer 2

Step-by-step explanation:

GIVEN :

Solution :

Given that

ABCD is a Parallelogram.

Given vertices of ABCD are and B (4,7), C (5,1) and D (10,-5).

Let the coordinates of the point A be (x,y)

We know that

In Parallelogram,the diagonals bisect to each other.

=> Mid point of AC = Mid point of BD

The coordinates of the mid point of the linesegment joining points (x1, y1) and (x2, y2) is

((x1+x2)/2, (y1+y2)/2 )