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a=1, b=10, c=3, d=2

5 (1c) Write answers on this side and show work on pages following this one numbered 1120,1121 , etc. using as many as you need. Define: $S:={(x,y)∈R_{2}∣ax+by+c=0}$ My $S:={(x,y)∈R_{2}∣()x+()y+()=0}$ Note that $P$ and $Q$ are required to be distinct points. 1 (i) Find $P:=(p_{1},p_{2})=(,)∈S$ and prove your asertion. 1 (ii) Find $Q:=(q_{1},q_{2})=(,)∈S$ and prove your assertion. 3 (iii) Decide if $S=SL(P,Q)$ that is, if the striaght line through the points $P$ and $Q$ is precisely the set $S$.

Let us consider the given problem:

Now, incorporating the given values of and we have .

1.(i) as .

Hence, the point is in .