Question

PQRS is a rhombus.Its diagonals PR and QS intersect at the pint M and satisfy QS= 2 PR. If its coordinates of S andM are(1,1) and (2,-1) respectively,find the coordinates of P ?​

Answer 1

Its diagonals PR and QS intersect at the point M and ... If the co- ordinates of S and M are (1,1) and (2,-1) ... Find the co-ordinates of P ... putting coordinates of M. 1 ...

Answer 2

PLEASE... MARKS...ME...AS...

........ BRILLIANTLIST

PQRS is a rhombus and its diagonals PR and SQ intersect at M and satisfy QS=2PR.If the coordinates of S and M are (1,1),(2,1) respectively find the coordinates of P

coordinates of S (1,1) and M (2,1)

Length of SM  = √((2-1)² + (1-1)²) = √1 + 0 = 1

SM = 1

QS = 2*SM = 2  as diagonal of rhombus bisect each other perpendicularly

QS = 2PR

=> 2 = 2PR

=> PR = 1

=> PM = PR/2 = 1/2

SM =1   PM = 1/2

PS² = SM² + PM²

=> PS² = 1 + 1/4

=> PS² = 5/4

Let say co-ordinates of P (x,y)   & S (1,1)

PS² = (x-1)² + (y-1)²

(x-1)² + (y-1)² = 5/4   eq1

Let say co-ordinates of P (x,y)   & M (2,1)

PM² = (x-2)² + (y-1)²

(x-2)² + (y-1)² = 1/4   eq2

eq 2 - eq 1

=> (x-2)² - (x-1)² = 1/4  - 5/4

using a² - b² = (a +b)(a-b)

=> (x - 2 + x -1) (x -2 -x +1) = -1

=> (2x -3)(-1) = -1

dividing by -1 both sides

=> 2x -3 = 1

=> 2x = 4

=> x = 2

putting x =1  in (x-2)² + (y-1)² = 1/4

(2-2)² + (y-1)² = 1/4

=>  (y-1)² = 1/4

square rooting both sides

=> y - 1 = ±1/2

=> y = 1/2 or 3/2

Co-ordinates of P  ( 2 ,  1/2)  or (2  , 3/2)