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# Coordinate Geometry CBSE NCERT Notes Class 10 Maths Chapter 7 PDF

## Coordinate Geometry

Coordinate geometry has been developed as an algebraic tool for studying geometry. It helps us to study geometry using algebra, and understand algebra with the help of geometry.

## Distance Formula

The distance between the points A(x_{1}, y_{1}) and B(x_{2}, y_{2}) is **|AB| = √[(x _{2} – x_{1})^{2} + (y_{2} – y_{1})^{2}]**

### Class 10 Maths Chapter 7 Examples 1:

Show that the points (1, 7), (4, 2), (–1, –1) and (– 4, 4) are the vertices of a square.

Let A(1, 7), B(4, 2), C(–1, –1) and D(– 4, 4) be the given points. Then,

Since AB = BC = CD = DA and AC = BD, all the four sides of the quadrilateral ABCD are equal and its diagonals AC and BD are also equal. Therefore, ABCD is a square.

## Section Formula

The coordinate of the points dividing the line segment joining the points **A(x _{1}, y_{1})** and

**B(x**

_{2}, y_{2})**internally**in the ratio of

**m:n**is

The coordinate of the points dividing the line segment joining the points **A(x _{1}, y_{1})** and

**B(x**

_{2}, y_{2})**externally**in the ratio of

**m:n**is

### Class 10 Maths Chapter 7 Examples 2:

Find the coordinates of the point which divides the line segment joining the points (4, –3) and (8, 5) in the ratio 3 : 1 internally.

Using the section formula, we get

Thus, (7, 3) is the required point.

## Area of Triangle

The area of triangle whose coordinates are **A(x _{1}, y_{1})**,

**B(x**then

_{2}, y_{2}) and C(x_{3}, y_{3})### Class 10 Maths Chapter 7 Examples 3:

Find the area of a triangle whose vertices are (1, –1), (– 4, 6) and (–3, –5).

Area of the triangle formed by the vertices A(1, –1), B(– 4, 6) and C (–3, –5) is

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