Students can go through AP SSC 10th Class Maths Notes Chapter 7 Coordinate Geometry to understand and remember the concepts easily.

## AP State Syllabus SSC 10th Class Maths Notes Chapter 7 Coordinate Geometry

→ The branch of mathematics which deals with points in a coordinate plane is called Coordinate/Analytical geometry.

→ There is a definite one-one correspondence between the position of a point in a plane and a pair of numbers called coordinates.

→ In a Cartesian plane, the position of a point P is determined by two coordinates x and y, where x is the distance of P from Y – axis and y is the distance of P from X – axis. So we denote it by P (x, y).

→ Signs of coordinates in different quadrants:

→ The point of intersection of the axes is called the- origin represented by (0, 0).

→ Any point lying on X – axis is denoted by (x, 0) as its y-coordinate is zero.

→ A point on Y – axis is denoted by (0, y) as its x-coordinate is zero.

→ Distance between any two points P(x_{1}, y_{1}) and Q(x_{2}, y_{2}) is given by

PQ = \(\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}\)

→ Distance between any two points P(x_{1}, 0) and Q(x_{2}, 0) on the X – axis is | x_{2} – x_{1} |.

Distance between any two points P(0, y_{1}) and Q(0, y_{2}) on the Y – axis is | y_{2} – y_{1} |

→ The coordinates of the point P which divides the line joining of two points (x_{1}, y_{1}) and (x_{2}, y_{2}) internally in the ratio m_{1} : m_{2} is

→ The midpoint of a line joining any two points (x_{1}, y_{1}) and (x_{2}, y_{2}) is

→ If the ratio in which ‘P’ divides two points (x_{1}, y_{1}) and (x_{2}, y_{2}) is k : 1, then

→ The point of concurrence of medians of a triangle is called its centroid.

→ Centroid divides each median in the ratio 2 : 1.

→ If (x_{1}, y_{1}), (x_{2}, y_{2}) and (x_{3}, y_{3}) are the vertices of a triangle, then its centroid is

→ The points P, Q on a line segment \(\overline{\mathrm{AB}}\) are said to be the points of trisection, if P and Q divides \(\overline{\mathrm{AB}}\) into three equal points i.e., AP = PQ = QB.

→ If P, Q are points of trisection of \(\overline{\mathrm{AB}}\), then P divides AB in the ratio 1 : 2 and Q divides AB in the ratio 2 : 1.

→ Area of a triangle AOB formed by the points origin O(0, 0), a point on X – axis A (x, 0) and another point on Y – axis B(0, y) is \(\frac{1}{2}\)xy.

→ If (x_{1}, y_{1}), (x_{2}, y_{2}) and (x_{3}, y_{3}) are the vertices of a triangle, then its area is

→ If three points are collinear, then the area of the triangle formed by these points is zero.

→ Let A (x_{1}, y_{1}), B (x_{2}, y_{2}) and C (x_{3}, y_{3}) are the vertices of a triangle △ABC, then AB = c; BC = a and AC = b and

S = \(\frac{a+b+c}{2}\)(semi-perimeter)

Then area of △ABC = \(\sqrt{S(S-a)(S-b)(S-c)}\)

This is called Heron’s formula.

→ Let ax + by + c = 0 represents a straight line; then any pair of coordinates (x_{1}, y_{1}) satisfying the linear equation ax + by + c = 0 is called its solution, i.e., if (x_{1}, y_{1}) is a solution of ax + by + c = 0 then ax_{1} + by_{1} + c = 0.

→ The inclination or angle made by a straight line with positive X-axis is called the slope of the straight line. Slope of a line joining any two points (x_{1}, y_{1}) and (x_{2}, y_{2}) is m = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

→ If ‘θ’ is the angle made by a line with X-axis, then slope m = tan θ.