1) ABCD is a parallelogram and the coordinates of A, B, C are (-8, -11), (1, 2) and (4, 3) respectively. Find the area of the parallelogram.

[i]i manage to find that D =( -5.-10) . area of parallelogram = AD x height i'm stuck here. how to find the height? i tried it by finding the angle between AB and AD first , (37.32 degree) then use it to find the vertical line from B. but i dont get the right answer.

2). Points A and C have coordinates (-1, 2) and (9, 7) respectively. A rectangle ABCD has AC as a diagonal. Calculate the possible coordinates of B and D if the length of AB is 10 units.

from the question, i know that AB=CD=10. the equation of line AB = x^2 +y^2+ 2x -4y-97=0. the equation of line CD= a^2 +b^2-18 a- 14b +30=0. then what should i do next?

3)If the five letters a, b, c, d, e are put into a hat, in how many ways could you draw two letters?

must we use permutation or combination? if permutation, why? why can't i use combination? 5C2?

4))3 balls are to be placed in 3 different boxes, not necessarily with 1 ball in each box. any box can hold up to 3 balls. find the number of ways the balls can placed if

i) they are all of the same colour

ii) they are all of different colours

i) what is wrong with my workings? 3C3 + (3C2 x 1C1) + 3C1?

ii) i have no clue at all for this. isnt it suppose to be the same as the first one?

5)GOLD MEDAL- if 2 D letters come first and the 2 L letters come last, find how many different arrangement there are

D D _ _ _ _ _ L L

5P5 x 2P2 x 2P2. why i dont need to permute the letter D and the L?

6) 3 letters are selected at random from the word "BIOLOGY" . Find the number that the selection contains one letter O

2C1 x 5C2 = 20 , the answer given is 5C2 = 10 , why i dont have to write 2C1?

7)The sum of the first 5 terms of a G.P. is twice the sum of the terms from the 6th to the 15th inclusive. Show that r^5 = 1/2 (SQRT3 -1).

S5 = 2 (S15 - S5)

a(1-r^5)/ i-r = 2a/ 1-r [(1-r^15)-(1-r^5)]

1 - r^5 = 2(r^5 -r^15)

2r^15-3r^5+1=0

let u=r^5

2u^3 - 3u +1=0

i'm stuck here. what to do next?