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Coordinate Geometry of Straight Lines (II) (quick)
The pictures for the desciptions of words are arranged in the ascending order.
PLease help me solve these types of questions , in a complete form.
Steps are required in a deeper depth.

(Use the analytic approach to answer the questions in this exercise. )

5. In the figure , the coordinates of P and Q are ( a, b ) and ( c , 0 ) respectively. M and N are points on OP and OQ respectively such that OM : MP = ON : NQ = 3:2 .
(a). Express the coordinates of M and N in terms of a , b and c .
(b). Prove that MN // PQ.

Level 2

6. In the figure , OABC and ODEF are two squares of sides a units and b units respectively. M is the mid-point of AF. MO is produced to meet CD at N. Prove that MN is perpendicular to CD .

7. It is given that ABCD is a parallelogram, M and N are the mid -points of AD and BC respectively. By placing ABCD on a rectangular coordinate plane, prove that BM // ND.

8. It is given that ABCD is a trapezium with angle A = angle B = 90 degree ,P,Q,R and S are the mid-points of AB, BC,CD and DA respectively, and K is the mid-point of PR.
(a) By placing ABCD on a rectangular coordinate plane , prove that S , K and Q are collinear.
(b) Is SK =KQ ? Explain your answer.

9. It is given that ABCD is a square,P and Q are points on AB and BC respectively such that AP : PB = BQ : QC. By placing ABCD on a rectangular coordinate plane, prove that AQ is perpendicular
to PD.

Answers: 5 . (a) M ; (3a/5 , 3b/5) , N : ( 3c/5 , 0 )

Level 2 8. (b) yes

Help is much grateful. THX.