Question

The origin O and the points P(4,1) , Q(5,5) and R(1,4) form a quadrilateral.
a) show that OR is parallel to PQ.
b) show that OP is parallel to RQ.
c) show that OP = OR.

I found the answers to a & b through the use of gradients. However i do not know what to do to solve c.

Answer 1

use the distance formula to show that the lengths are equal.

Answer 2

c)

The distance between two points:

d = √ [ ( x2 - x1 )² + ( y2 - y1 )² ]


Coordinates of the origin O ( 0 , 0 )


The distance between origin ( 0 , 0 ) and P ( 4 , 1 ) = OP

x1 = 0 , y1 = 0 , x2 = 4 , y2 = 1

d = √ [ ( x2 - x1 )² + ( y2 - y1 )² ] = OP

OP = √ [ ( 4 - 0 )² + ( 1 - 0 )² ]

OP = √ ( 4² + 1² ) = √ ( 16 + 1 ) = √17


The distance between origin ( 0 , 0 ) and R ( 1 , 4 ) = OR

x1 = 0 , y1 = 0 , x2 = 1 , y2 = 4

d = √ [ ( x2 - x1 )² + ( y2 - y1 )² ] = OR

OR = √ [ ( 1 - 0 )² + ( 4 - 0 )² ]

OR = √ ( 1² + 4² ) = √ ( 1 + 16 ) = √17


√17 = √17

OP = OR

Answer 3

THANK YOU!