Eight points A, B, C, D, E, F, G, and H are distributed in a plane. Exactly five of the points are on line L sub1, exactly three are on line L sub2, and exaactly three are on line L sub3. Are the three lines concurrent? Justify answer.
There are eight points...
three define L1
five define L2
three define L3
L3 has two points on either L2 or L1, making it concurrent with that line. The other point on L3 is on the other line, but since there is no evidence of another point, it is not concurent with the other line.
To determine if the three lines L1, L2, and L3 are concurrent, we need to analyze the given information about the distribution of points.
We know that exactly five points are on line L1, exactly three points are on line L2, and exactly three points are on line L3. Let's break down the possibilities:
1. If there are no common points between L1, L2, and L3, then the lines are not concurrent. In this case, L1, L2, and L3 would be parallel to each other.
2. If all three lines share a common point P, then the lines are concurrent. In this case, the three lines intersect at point P.
Now, let's consider the given scenario:
L1 has exactly five points.
L2 has exactly three points.
L3 has exactly three points.
From the given information, we can conclude that L3 must have two points on either L1 or L2 because there are only three points on L3. This means that L3 is concurrent with either L1 or L2.
However, since there is no evidence or information provided about another point on L3 that could be concurrent with the remaining line (L1 or L2), we cannot determine if all three lines are concurrent. Only L3 is concurrent with either L1 or L2.
To summarize, based on the given information, we cannot conclude with certainty if all three lines (L1, L2, and L3) are concurrent.