How many straight lines can be drawn using 10 points out of which 3 are collinear
ML Aggarwal Solutions Class 6 Mathematics Solutions for Basic Geometrical Concept Exercise 10 in Chapter 10 - Basic Geometrical ConceptQuestion 2 Basic Geometrical Concept Exercise 10 Show
How many lines can be drawn through three collinear points? Answer: A set of three or more points on the same straight line is known as a collinear point. Collinear points cannot exist on different lines but they can exist on different planes. Collinearity is the property of points being collinear. The Slope formula can be applied to identify if the points are collinear or not. Only one line can be drawn through three collinear points. Was This helpful?
There are 10 points in a plane of which 4 are collinear. How many different straight lines can be drawn by joining these points. Number of straight lines formed joining the 10 points, taking 2 points at a time = \[{}^{10} C_2 = \frac{10}{2} \times \frac{9}{1} = 45\] Number of straight lines formed joining the 4 points, taking 2 points at a time =\[{}^4 C_2 = \frac{4}{2} \times \frac{3}{1} = 6\] But, when 4 collinear points are joined pair wise, they give only one line. Concept: Combination Is there an error in this question or solution?
Solution : There are ten points `P_(1), P_(2),.., P_(10)`. There are 10 points in a place, no three of these points are in a straight line. What is the total number of straight lines which can be formed by joining the points?This question was previously asked in NDA (Held On: 21 Apr 2019) Maths Previous Year paper View all NDA Papers >
Answer (Detailed Solution Below)Option 2 : 45 Free Electric charges and coulomb's law (Basic) 10 Questions 10 Marks 10 Mins Concept If there are n points in a plane and no three points lie on a straight line, then the total number of straight line segments that can be formed is given by: \(C\left( {n,\;2} \right) = \frac{{{\rm{n}}!}}{{2!\left( {{\rm{n\;}} - {\rm{\;}}2} \right)!}}\) Calculation Given: n = 10. \(\Rightarrow \;C\left( {10,\;2} \right) = \frac{{10!}}{{2!\left( {10 - {\rm{\;}}2} \right)!}} = \frac{{10 \times 9}}{2} = 45\) Hence, the number of straight lines that can be formed is 45. Last updated on Nov 17, 2022 Union Public Service Commission (UPSC) has released the NDA Result I 2022 (Name Wise List) for the exam that was held on 10th April 2022. 519 candidates have been selected provisionally as per the results. The selection process for the exam includes a Written Exam and SSB Interview. Candidates who get successful selection under UPSC NDA will get a salary range between Rs. 15,600 to Rs. 39,100. Solution The correct option is D25Explanation for the correct option:We have been given that there are 10 points of which 7 are collinear.We know that to make a line we need at least 2 points. So, the number of ways to select 2 points from 10 points to make straight lines is C210 .As it is given that 7 points are collinear which means that we can’t make lines for all the 7 points. So, the number of ways to select 2 points from these 7 points which will not give any distinct line is C27So, we will subtract7C2 from C 210. But 7 collinear points are on a straight line. Therefore we have to add +1 in C2 10∴Total number of lines =C210-C2 7+1=10!2!8!-7!2!5 !+1∵Crn=n!r !n-r!=10×9×8!2×1×8!-7× 6×5!2×1×5!+1=45-21+1=46-21 =25Thus there are 25 straight lines that can be drawn out of 10 points of which 7 are collinear.Hence, option D is the correct answer.How many straight lines can be formed with 10 points if 5 are collinear?∴ total ways =10C2−5C2+1=45−10+1=36.
How many straight lines are possible with 3 points?Four lines can be drawn through 3 non-collinear points.
How many different triangles can be formed from 10 points in which 3 are collinear points?110 triangles can be formed by joining 10 points as vertices, in which n points are collinear.
How many straight lines can be drawn from 10 points out of which 4 are collinear?Hence, the total no. of ways of different lines formed are 40.
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