How many state lines can be formed by joining 12 points on a plane out of which no points are collinear?

How many state lines can be formed by joining 12 points on a plane out of which no points are collinear?

12C2 ways. ∴ The number of different straight lines that can be formed by joining the given 12 points. . 12C212×111×2=66.

How many lines are determined by 10 points no 3 of which are collinear?

Here there are 10 C 2 ways of forming straight line from 10 points if the no 3 points are collinear. 10 C 2=10!/(2! ×8!) =(10×9)/2=45 ans.

Are the 3 points collinear?

Three or more points are collinear, if slope of any two pairs of points is same. With three points A, B and C, three pairs of points can be formed, they are: AB, BC and AC. If Slope of AB = slope of BC = slope of AC, then A, B and C are collinear points.

Can 3 lines be collinear?

Three or more points that lie on the same line are collinear points . Example : The points A , B and C lie on the line m . They are collinear.

What are 3 points on a straight line?

Collinear Points Definition In a given plane, three or more points that lie on the same straight line are called collinear points.

How many straight lines can be obtained by joining 12 points?

Number of straight lines that can be formed using 12 points = 12C2 = 12×111×2 12 × 11 1 × 2 = 66.

How many triangles can be drawn by joining 12 points on a plane no three of which are in the same line?

n – r)! Hence, the total no. of triangles formed are 210.

How many straight lines can be formed by joining 12?

How many different straight lines can be formed by joining 12 different points on a plane of which four are collinear and the rest are non collinear? a. 16.

Do 3 points always determine a line?

Yes. repetition of a point three times is still a point. duplication of a point, and a different point, can determine a line.

How many lines are determined by 15 points no 3 of which are collinear?

Transcribed image text: How many lines are determined by 15 points, no 3 of which are collinear? The number of lines is 17 Suppose 10 fair coins are tossed.

How many points in a plane are collinear?

There are 12 points in a plane, out of which 3 points are collinear. How many straight lines can be drawn by joining any two of them? There are 12 points in a plane, out of which 3 points are collinear. How many straight lines can be drawn by joining any two of them?

How to count the number of lines in a collinear group?

Let’s divide the points in two groups: the collinear group of 4 points, and the non-collinear group of 6 points. To count the number of lines, we have three possible cases. First, the lines formed using the points of the collinear group – only 1 line. Second, the lines formed using only the points of the non-collinear group – 6 C 2 or 15 lines.

How many distinct lines does a set of 12 points have?

Any 2 points determine a line. So the number of lines is the number of distinct pairs out of 12 points. No 3 are collinear, which means no two pairs define the same line, so all these lines are distinct. (3 collinear points will have 3 pairs of points. all defining the same line)

How many lines are there in 12×11?

There are 66 lines. As no 3 points are co-linear, every line passes through exactly two of the points. Thus every point is joined by one of the lines to every other point. So it looks like there are 12 × 11 = 132 lines.