Question

the diagram shows several points and lines.
which statements are true based on the diagram?
select two options.
points k, m, and n are collinear.
points j, k, and q are collinear.
point r is the intersection of line kn and line mq.
lines jq, km, and mq all intersect at point k.
there is only one line that can be drawn through points l and p.

Explanation:

1. Collinearity check for J, K, Q: Collinear points lie on the same straight line. Observing the diagram, points J, K, and Q are on a single straight line, so this statement is true.
2. Unique line through L and P: A fundamental geometric postulate states that exactly one straight line can be drawn through any two distinct points. Since L and P are distinct, this statement is true.
3. Eliminating other options:

• K, M, N are not on a single line, so they are not collinear.
• The intersection of line KN and line MQ is point N, not R.
• Line MQ does not pass through K, so the three lines do not all intersect at K.

Answer:

B. Points J, K, and Q are collinear.
E. There is only one line that can be drawn through points L and P.