Question

1. How many lines can be drawn through a given point ?

2. In how many points two distinct lines can intersect ?

3. In how many lines tow distinct planes can intersect ?

4. In how many least no. of distinct points determine a unique plane ?

5. If B lies between A and C and AC=10, BC=6, what is AB² ?

Answer 1

$$\begin{gathered} 1) \\ \mathrm{As}\mathrm{we}\mathrm{know}\mathrm{from}\mathrm{Euclid}\text{'}\mathrm{s}\mathrm{axioms}\mathrm{that}\mathrm{Infinte}\mathrm{number}\mathrm{of}\mathrm{lines}\mathrm{can}\mathrm{be}\mathrm{drawn}\mathrm{from}\mathrm{given}\mathrm{point} \\ 5) \\ \mathrm{As}\mathrm{we}\mathrm{know}\mathrm{that}\mathrm{from}\mathrm{Euclid}\text{'}\mathrm{s}\mathrm{axioms}, \\ \mathrm{AC}+\mathrm{BC}=\mathrm{AB} \\ \mathrm{Things}\mathrm{which}\mathrm{coincide}\mathrm{with}\mathrm{one}\mathrm{another}\mathrm{aree}\mathrm{qual}\mathrm{to}\mathrm{one}\mathrm{a}\mathrm{nother}. \\ \mathrm{So}\mathrm{AB}=10+6=16 \\ \mathrm{So}{\mathrm{AB}}^2={16}^2=256. \end{gathered}$$