How do you show that three points are collinear using the formula?
Expert Answer:
- We need to prove the points (3,-2),(5,2) and(8,8) are collinear.
- A=(3,-2) B=(5,2) C=(8,8)
- Let The points B divides AC in the ratio of k:1.
- Then the coordinates will be,
- Coordinates of B are (5,2)
- Comparing we get,
- Value of k is same in both.
- Therefore Points A,B,C are collinears.
In what ratio is the line segment joining the points (- 2 3 and 3/7 is divided by Y axis also find the coordinates of division?
We will now use the section formula. So, the required ratio in which the y axis divides the line joining the points (-2, -3) and (3, 7) is 2 : 3. Hence, option (c) is correct.
What is the use of section formula?
In coordinate geometry, Section formula is used to find the ratio in which a line segment is divided by a point internally or externally. It is used to find out the centroid, incenter and excenters of a triangle. In physics, it is used to find the center of mass of systems, equilibrium points, etc.
How do you know if 3 points are collinear 10?
Sol: If the A, B and C are three collinear points then AB + BC = AC or AB = AC – BC or BC = AC – AB. If the area of triangle is zero then the points are called collinear points. If three points (x1, y1), (x2, y2) and (x3, y3) are collinear then [x1(y2 – y3) + x2( y3 – y1)+ x3(y1 – y2)] = 0.
What is the section formula for three points that are collinear?
If three points are collinear, then one of the points divide the line segment joining the other two points in the ratio r : 1. The section formula can be used only when the given three points are collinear. Using section formula, show that the points A (7, −5), B (9, −3) and C (13, 1) are collinear.
How do you know if a line is collinear?
Using Slope Formula Three or more points are said to be collinear if the slope of any two pairs of points is the same. The slope of the line basically measures the steepness of the line. Suppose, X, Y and Z are the three points, with which we can form three sets of pairs, such that, XY, YZ and XZ are three pairs of points.
What are collinear and non-collinear pairs?
Since you can draw a line through any two points there are numerous pairs of points that are collinear in the diagram. A set of points that are non-collinear (not collinear) in the same plane are A, B, and X. A set of points that are non-collinear and in different planes are T, Y, W, and B. 1.
How to find the section formula for three points?
The section formula can be used only when the given three points are collinear. Example 1 : Using section formula, show that the points A (7, −5), B (9, −3) and C (13, 1) are collinear. Solution : Section formula = (mx 2 +nx 1) / (m+n), (my 2 +ny 1) / (m+n) Let the point B divides the line segment joining the point A and C in the ratio k : 1