# Formulas To Solve Coordinate Geometry Questions

## Formulas For Coordinate Geometry

Coordinate geometry is a branch of geometry where the position of the points on the plane is defined with the help of an ordered pair of numbers also known as coordinates.

### Coordinate Geometry Formulas and Basic Concept

• The point of intersection of the x and the y-axis is known as the origin. At this point, both x and y are 0.
• The values on the right-hand side of the x-axis are positive and the values on the left-hand side of the x-axis are negative.
• Similarly, on the y-axis, the values located above the origin are positive and the values located below the origin are negative. ### Formulas for Coordinate Geometry.

• Distance between two points A(x1, y1) and B(x2, y2)
AB = √(x2-x1 )2+(y2-y1 )2
• Slope of line when two points are given (x1, y1) and (x2, y2)
m = (y1-y2)/(x1-x2 )
• Slope of line when linear equation is given ax + by = c => -a/b
• Midpoint = (x1+x2)/2, (y1+y2)/2
• The co-ordinates of a point R(x,y) that divides a line segment joining two points A(x1, y1) and B(x2, y2) internally in the ratio m:n is given by
x = (mx2+nx1)/(m+n); y = (my2+ny1)/(m+n)
• The co-ordinates of a point R(x,y) that divides a line segment joining two points A(x1, y1) and B(x2, y2) externally in the ratio m:n is given by
x = (mx2-nx1)/(m-n); y = (my2-ny1)/(m-n)
• Centroid of a triangle with its vertices (x1,y1), (x2,y2), (x3,y3)
C = (x1+x2+x3)/3, (y1+y2+y3)/3
• Area of a Triangle with its vertices A(x1,y1), B(x2,y2), C(x3,y3)
A = 1/2 ((x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2))
• Division of a line segment by a point
If a point p(x, y) divides the join of A(x1, y1) and B(x2, y2), in the ratio m: n, then
x= (mx2 + nx1)/m + n and y= (my2 + ny1)/m + n
• The equation of a line in slope intercept form is Y= mx+ c, where m is its slope.
The equation of a line which has gradient m and which passes through the point (x1, y1) is =
y – y1 = m(x – x1)