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: Recall collinear - point definition

Collinear points lie on the same straight - line.

Step2: Check points K, M, N

From the diagram, points K, M, N do not lie on the same line, so the statement "Points K, M, and N are collinear" is false.

Step3: Check points J, K, Q

Points J, K, Q lie on the same straight - line, so the statement "Points J, K, and Q are collinear" is true.

Step4: Check intersection of lines

Point R is not the intersection of line KN and line MQ. The intersection of line KN and line MQ is point N. So the statement "Point R is the intersection of line KN and line MQ" is false.

Step5: Check intersection of multiple lines

Lines JQ, KM, and MQ do not all intersect at point K. Line JQ and KM intersect at K, but MQ does not intersect them at K. So the statement "Lines JQ, KM, and MQ all intersect at point K" is false.

Step6: Recall line - through - two - points property

According to the postulate, there is exactly one line that can be drawn through two distinct points. So the statement "There is only one line that can be drawn through points L and P" is true.

Answer:

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