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.
3 answers
use the distance formula to show that the lengths are equal.
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
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
THANK YOU!
1 answer