How many straight lines can be drawn from a points?
 How many straight lines can be drawn through two distinct points?Answer: One Step by Step Explanation:
Let us consider the 2 points as A and B. Now, infinite lines can pass through the point A as shown below. 3 Lines 5 Lines 6 Lines \[\therefore \](4 - 1) (4 - 1) + (4 - 2) (4 - 1) + (4 - 2) + (4 - 3) + (4 - 4) \[\therefore \]They are of the form: \[\begin{align} & h=\sum\limits_{i=1}^{n}{\left( n-i \right)}=\left( n-1 \right)+\left( n-2 \right)+\left( n-3 \right)+.....+\left( n-n \right) \\ & =\sum\limits_{i=1}^{n}{n}-\sum\limits_{i=1}^{n}{i}\Rightarrow L={{n}^{2}}-\dfrac{n\left( n+1 \right)}{2}=\dfrac{2{{n}^{2}}-{{n}^{2}}-n}{2} \\ & L=\dfrac{{{n}^{2}}-n}{2}=\dfrac{n\left( n-1 \right)}{2} \\ \end{align}\] \[\therefore L=\dfrac{n\left( n-1 \right)}{2}\], where L = number of lines. So, for 4 points, n=4, \[L=\dfrac{4\left( 4-1 \right)}{2}=\dfrac{4\times 3}{2}=6\]lines. Where n=1, \[L=\dfrac{1\left( 1-1 \right)}{2}=\dfrac{0}{2}\]i.e. Infinite number of lines. Where n=2, \[L=\dfrac{2\left( 2-1 \right)}{2}=1\]etc. Hello Welcome to Lido learning today we are going to see a question that is to write how many lines can be drawn through These four statements are there how many lines can be drawn from a given point if you take a point over here At any point, you take this point sorry take any point or here one point if you take any point how many lines can be drawn you can draw like this you can draw like this you can draw like this also you can draw new anime like this if you can draw infinite points in finite infinite points for this also we can draw any points Any angle we can keep and we can draw any lines so infinite points for the first one, the answer is infinite We will go with the second case The second case is this is the first one, the second one is two given fixed points if you are given two fixture points is given to given fixed points how many lines can you draw you can draw only one line throws it you cannot draw like this if you draw like this it will go away you cannot like this you can only draw one line okay you can only draw one line I'm going to save okay two-pixel points where you draw one line okay so only one line is possible only one line is possible one line then comes the third case. The third case is three collinear points three colonial point is collinear means lying on a same line these three colonial points how many lines you can draw only one line through it Okay, this is also one line if you take the other case the fourth one three non-collinear points we take three Non-colonial points one point here, one point here, one the point can you draw number of lines passing through the same point is not, we cannot draw the The line will not be like this right the violin will be like this so the a line will only be in the straight line so no points can be drawn, no lines can be drawn to this The answers are infinite lines one line one line and no lines I hope you understand this video if you have any doubts, you can put them down. the comment section and thank you for watching this gave How many straight lines can be drawn between five points (A, B, C, D, and E), no three of which are colinear? Attempt: Given 5 points, a line consist always of 2 points. Thus the total number of straight lines that can be drawn between 5 points is 5_C_2 = 10. Is this correct? Thank you. |
