Question

If there are nine straight lines, of which five are concurrent at a point and the other four are concurrent at another point, and no two of these nine lines are parallel, then the number of points of intersection is equal to:

a) 36
b) 45
c) 54
d) 63

Answer 1

The number of points of intersection between the nine lines is 36. The correct answer is a) 36.

Step-by-step explanation:

The subject of this question is mathematics, specifically geometry involving the properties and intersections of straight lines. To calculate the number of points of intersection for nine straight lines where five are concurrent at one point and four are concurrent at another, we need to consider the following:

Each of the five lines that are concurrent at one point will not intersect with each other at any point other than that point of concurrency.

The same is true for the other set of four lines that are concurrent at another point.

Every line from the group of five lines can intersect with every line from the group of four lines. This gives us 5 * 4 = 20 points of intersection between the two groups.

To find the number of points of intersection, we need to determine the maximum number of intersections that can occur between the nine lines. For any two lines, they can intersect at most once. Therefore, the total number of intersections between the nine lines can be calculated as follows:

Number of intersections = (Number of lines) × (Number of lines - 1) / 2

Plugging in the given values, we get:

Number of intersections = (9 × 8) / 2 = 36

Therefore, the correct answer is a) 36.