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2(a) Line AB equation is

y = 2x + c where c is a constant

Since point A is ( -1, 3)

3 = -2 + c

c= 5

Line AB is y = 2x + 5 ————(1)

(b) Line BC is y = -2x+ 17 ————–(2)

(1) + (2) :

2y = 22

y = 11

11 = 2x + 5

x = 3

Coordinate of B is ( 3, 11)

(c) AE = ( 4 , 12) = AO  + OE  = ( 1, -3) + OE 

OE = ( 3, 15)

So coordinate of E is ( 3, 15).

(d) (i)  DE = DO + OE = ( -3 , -7) + ( 3, 15) = ( 0, 8)

(ii) DB = DO + OB = ( -3 , -7) + ( 3, 11) = ( 0, 4)

(e)  X coordinates of D, E and B are 3, so these points are on the same straight line parallel to y axis at x = 3. 

DEB cannot form a triangle. 

 

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Thank you very much.

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