Condition for Collinearity of Three Points
Let the given points be A(x1, y1), B(x2, y2), and C(x3, y3). Then A, B, and C are collinear,
area of ABC = 0
1/2[x1(y2 – y1) + x2(y3 – y1) + x3(y1 – y2)] = 0
Example: Show that points A(-1, 1), B(5, 7), and C(8,10) are collinear.
Solution:
Let A(-1, 1), B(5, 7) and C(8, 10) be the given points.
Then, (x1 = -1, y1 = 1), (x2 = 5, y2 = 7) and (x3 = 8, y3 = 10)
∴ x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2)
= (-1) (7 – 10) + 5(10 -1) + 8(1 – 7)
= (3 + 45 – 48)
= 0
Hence, the given points are collinear.
Coordinate Geometry
Coordinate geometry is the branch of mathematics that deals with plotting the curve on the coordinate axes. Various curves can be plotted on the coordinate plane using coordinate geometry formulas. Co-ordinate geometry uses algebraic equations to plot various curves on the coordinate plane. One of the popular coordinate systems used in mathematics is the rectangular Cartesian system.
Table of Content
- What is Coordinate Geometry?
- Coordinates of a Point
- Distance Formula
- Mid-Point Formula
- Section Formula
- Slope Formula
- Area of Triangle
- Condition for Collinearity of Three Points
- Centroid of a Triangle