Section Formula
The coordinates of the point P(x, y) which divides the line segment joining A(x1, y1) and B(x2, y2) internally in the ratio m:n are given by
x = (mx2 + nx1) / (m+n)
y = (my2+ny1) / (m+n)
Example: Find the coordinates of the point that divides the line segment joining the points A(5, 4) and B(7,8) in the ratio of 2:3.
Solution:
Let M(x, y) be the required point,
given m:n = 2:3 and (x1, y1) = (5, 4) , (x2, y2) = (7,8)
now for M(x,y)
x = (mx2 + nx1) / (m+n)
= (2×7 + 3×5)/(2 + 3)
= 29/5
y = (my2+ny1) / (m+n)
= (2×8 + 3×4)/(2 + 3)
= 40/5
= 8
So, the required point M(x,y) is (29/5 , 8)
Read More about Section Formula.
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