The vertices of parallelogram are -2,3 3,-1 p,q -1,9 find the value of p and q
Answers
Step-by-step explanation:
Given :-
The vertices of parallelogram are (-2,3),(3,-1),( p,q) and (-1,9).
To find :-
Find the value of p and q ?
Solution :-
Given that :
The vertices of parallelogram are (-2,3),(3,-1),( p,q) and (-1,9).
Let A = (-2,3)
Let B = (3,-1)
Let C = ( p,q)
Let D = (-1,9)
We know that
The diagonals bisect to each other in a Parallelogram.
AC and BD are diagonals in ABCD paralellogram.
AC and BD bisects to each other.
=> The mid point of AC = The mid point of BD
Mid point of AC :-
Let (x1, y1) = A (-2,3) => x1 = -2 and y1 = 3
Let (x2, y2) = C ( p,q) => x2 = p and y2 = q
We know that
The coordinates of the mid point of the linesegment joining the points (x1,y1) and (x2, y2)
is ( { x1+x2}/2 , {y1+y2}/2 )
Mid Point of AC = ( {-2+p}/2 , {3+q}/2 )
Mid point of BD :-
Let (x1, y1) = B (3,-1) => x1 = 3 and y1 = -1
Let (x2, y2) = D (-1,9) => x2 = -1 and y2 = 9
We know that
The coordinates of the mid point of the linesegment joining the points (x1,y1) and (x2, y2)
is ( { x1+x2}/2 , {y1+y2}/2 )
Mid Point of BD = ( {3-1}/2 , {-1+9}/2 )
=> Mid point of BD = ( 2/2 , 8/2)
=> Mid point of BD = (1,4)
We have
The mid point of AC = The mid point of BD
=> ( {-2+p}/2 , {3+q}/2 ) = (1,4)
On Comparing both sides then
=> {-2+p}/2 = 1 and {3+q}/2 = 4
=> (-2+p) = 1×2 and (3+q) = 4×2
=> -2+p = 2 and 3+q = 8
=> p = 2+2 and q = 8-3
=> p = 4 and q = 5
Therefore, p = 4 and q = 5
Answer:-
The values of p and q are 4 and 5 respectively.
Used Concept :-
The diagonals bisect to each other in a Parallelogram.
Used formulae:-
The coordinates of the mid point of the linesegment joining the points (x1,y1) and (x2, y2) is ( { x1+x2}/2 , {y1+y2}/2 )