Answer:
a) H,N,K and I.
b) The line p.
c) The line r.
d) The line q can be also named putting the symbol '' ↔ '' over the capital letters JL, JK or KL.
e) The point N.
Explanation:
Let's study each item in order to answer the question :
a) Four collinear points :
We know that two or more points are called ''collinear points'' wherever they belong to the same line.
In the diagram, the only line that contains four points which have name is the line r. The four points are H,N,K and I.
b) A line that contains point M :
In this case, the only line that contains to the point M is the line p because the point M is situated over the line p.
c) A line that contains points H and K :
The only line that contains both points is the line r because the points H and K are situated over the line r.
d) Another name for line q :
Another way to name any line is putting the symbol ''↔'' over a pair of points that are situated over the line (Let's remember that we write the points with capital letters).
One possible name for the line q can be written putting ''↔'' over JL.
The other two names can be written putting ''↔'' over the capital letters JK or KL.
e) The intersection of lines p and r :
There are three cases of intersection between lines :
1 - The case in which the lines don't intersect at any point at all.
2 - The case in which the lines intersect at one point.
3 - The case in which the lines intersect at infinite points (for this case, the lines are parallel and there are superimposed).
In this case, the intersection of the lines p and r is the point N (which belongs to both lines).