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:

Step1: Analyze collinearity

Collinear points lie on the same straight - line. Points \(K\), \(M\), and \(N\) do not lie on the same straight - line. Points \(J\), \(K\), and \(Q\) do not lie on the same straight - line.

Step2: Analyze intersection

Point \(R\) is not the intersection of line \(KN\) and line \(MQ\). Lines \(JQ\), \(KM\), and \(MQ\) do not all intersect at point \(K\).

Step3: Use the postulate of a line through two points

According to the postulate that exactly one line can be drawn through two distinct points, there is only one line that can be drawn through points \(L\) and \(P\).

Answer:

There is only one line that can be drawn through points \(L\) and \(P\).