P (4, 2) and Q (-1, 5) are the vertices of parallelogram PQRS and (-3, 2) are the co-ordinates of the point of intersection of its diagonals. Find co-ordinates of R and S.

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Solution

Let the co-ordinate of R and S be (x,y) and 9a,b0 respectively

$M i d space p o i n t space o f space P R space i s space O O left parenthesis negative 3 comma 2 right parenthesis equals O open parentheses fraction numerator 4 plus x over denominator 2 end fraction comma fraction numerator 2 plus y over denominator 2 end fraction close parentheses minus 3 equals fraction numerator 4 plus x over denominator 2 end fraction comma space 2 equals fraction numerator 2 plus y over denominator 2 end fraction minus 6 equals 4 plus x space space comma space 4 equals 2 plus y x equals negative 10 space space comma y equals 2 H e n c e space R equals left parenthesis negative 10 comma 2 right parenthesis S i m i l a r l y space comma t h e space m i d space p o i n t space o f space S Q space i s space O t h e r e f o r e space O 9 minus 3 comma 2 right parenthesis equals O open parentheses fraction numerator a minus 1 over denominator 2 end fraction comma fraction numerator b plus 5 over denominator 2 end fraction close parentheses minus 3 equals fraction numerator a minus 1 over denominator 2 end fraction space space comma 2 equals fraction numerator b plus 5 over denominator 2 end fraction minus 6 equals a minus 1 space comma space 4 equals b plus 5 a equals negative 5 space space comma b equals negative 1 h e n c e space S equals left parenthesis negative 5 comma negative 1 right parenthesis T h u s space comma t h e space c o minus o r d i n a t e s space o f space t h e space p o i n t space r space a n d space S space a r e space left parenthesis negative 10 comma 2 right parenthesis space a n d space left parenthesis negative 5 comma negative 1 right parenthesis$

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Similar questions

P (–10, 2) and Q (–5, –1) are the vertices of a parallelogram PQRS. The coordinates of the point where the diagonals intersect are (–3, 2). Find the coordinates of R and S.

Q. The extremities of the diagonal of a square are the points (1,5) and (8 , 8). Find the equation to its sides and the co-ordinates of the other vertices.

Q. The co-ordinates of the vertices of

□ P Q R S

are

P (- 1, 2), Q (- 4, - 2), R (- 4, - 3)

and

S (- 1, - 5)

respectively. Draw

□ P Q R S

and state it is which type of quadrilateral.

P \equiv (1, - 9)

Q \equiv (2, 5)

and

R \equiv (6, 7)

are the co-ordinates of the vertices of

△ P Q R

, then find the co-ordinates of the centroid from the following alternatives given:

Q. Show that

□

PQRS is a rectangle if P (

-

2,6), Q(3,1), R(

-

-

3) and S(

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6,2) are the co-ordinates of the vertices.

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