- In coordinate geometry, the tools of algebra are used in studying geometry by establishing 1-1 correspondence between the points in a plane and the ordered pairs of real numbers.
- If P(x1,y1) and Q(x2,y2) be any two points in the plane, then
- If A(x1,y1), B(x2,y2) and C(x3,y3) be the vertices of a triangle, then area, D, of triangle ABC is given by
- The points A, B and C are collinear if and only if area of triangle ABC is zero.
- A point R is said to divide PQ internally in the ratio m:n if R is within
- If R(x,y) divides the join of P(x1,y1) and Q(x2,y2) internally in the ratio m:n, then
A point R is said to divide PQ externally in the ratio m:n, where m
¹ n, if R is outside PQ and 
- If R(x,y) divides the join of P(x1,y1) and Q(x2,y2) externally in the ratio m:n, where m ¹ n, then
- If M(x,y) is the midpoint of the join of P(x1,y1) and Q(x2,y2), then
- If A(x1,y1), B(x2,y2) and C(x3,y3) are the vertices of a triangle, then
- Centroid =
- Incentre =
where a = BC, b = CA, c = AB
- When a point moves so as to always satisfy a given condition or conditions, the path it traces out is called its locus under these conditions.
- If P(x,y) be any sample point on the locus, then an equation involving x and y which is satisfied by each point on the locus and such that each point satisfying the equation is on the locus is called the equation of the locus.
- The slope of a non-vertical line is defined as the tangent of the angle which the line makes with the positive direction of the x-axis.
- If a non-vertical line passes through two distinct points (x1,y1) and (x1, y1), then the slope, m, of the line is given by
- The slope of a horizontal line is zero.
- The slope of a line making equal intercepts on the axes is '-1'.
- The slope of a line equally inclined to the axes is either '1' or '-1'.
- The slope of the line ax + by + c = 0, b ¹ 0 is equal to
- Two non-vertical lines are parallel if and only if their slopes are equal.
- Two non-vertical lines are perpendicular if and only if the product of their slopes is '-1'.
