Question

Show that quadrilateral pqrs formed by P(1,-2),Q(5,2),R(3,-1), S( - 1, -5 )is a parallelogram

Answer 1

Answer:

prove that oppo sides are equal

Answer 2

The diagonals of a parallelogram bisect each other

The cordinates of the midpoint of PR =the cordinates of the midpoint of SQ

PQRS is a parallelogram

Step-by-step explanation:

quadrilateral pqrs formed by P(1,-2),Q(5,2),R(3,-1), S( - 1, -5 )

we have to prove that it is a parallelogram

since  we know that the diagonals of a parallelogram bisect each other

we need to find the mid point of the diagonals of quadrilateral PQRS

the cordinates of the midpoint of PR =the cordinates of the midpoint of SQ

so the cordinates of the midpoint of PR =

$\frac{x_1 + x_2 }{2} , \frac{y_1+y_2}{2}$

=$(\frac{1+3}{2},\frac{-2-1}{2})$

= $(\frac{4}{2},\frac{-3}{2})$

=$(\frac{2}{1},\frac{-3}{2})$

the cordinates of the midpoint of SQ =

$\frac{x_1 + x_2 }{2} , \frac{y_1+y_2}{2}$

=$(\frac{5-1}{2},\frac{2-5}{2})$

= $(\frac{4}{2},\frac{-3}{2})$

=$(\frac{2}{1},\frac{-3}{2})$

the cordinates of mid point of PR is equal to cordinates of midpoint of SQ

hence, PQRS is a parallelogram

#Learn more:

https://brainly.in/question/6975480