Question

The following design shows a hexagon ABCDEF used in designing a carpet. The coordinates are
A(2,1), B(-1,2) , C(3,3) , D(5,2) , E(2,0) , F (1,1)


(i) Find the length of side AB.
a) 3 √2 b) √10 c) 4 d) 5
(ii) Midpoint of side AB is
a) (3,3) b) (1,2) c) (0.5,1.5) d) (1.5,0.5)
(iii) Point which divides the line joining DE in the ratio 2:1 is
a) (3,2) b) (2,3) c) (3,2/3) d) (2/3,3)
(iv) Find the length of the side AF
a) √10 b) 3√2 c) 1 d) 5
(v) Midpoint of side AD is
a) (3 ,7) b) (3/2 ,7/2) c) (7/2, 3/2) d) (7,3)

Answer 1

Answer:

(i) distance = root (x2-x1)² + (y2-y1)²

AB=root of (-1-2)²+(2-1)²

= root of (-3)²+(1)²

= root of 9+1

AB = root 10

(ii) mid point of AB = (x1+x2/2,y1+y2/2)

= (2+(-1)/2,1+2/2)

= (1/2,3/2)

= (0.5,1.5)

(iv) is also same as (i)

(v) is also same as (ii)

(iii) internally formula is (m2x1+m1x2/m1+m2,m2y1+m1y2/m1+m2)