# What are the formulas in coordinate geometry?

## What are the formulas in coordinate geometry?

Coordinate Geometry Formulas List for Classes 9, 10 and 11

All Formulas of Coordinate Geometry | |
---|---|

Slope Intercept Form of a Line | y = mx + c |

Point-Slope Form | y − y1= m(x − x1) |

The slope of a Line Using Coordinates | m = Δy/Δx = (y2 − y1)/(x2 − x1) |

The slope of a Line Using General Equation | m = −(A/B) |

**How many formulas are there in coordinate geometry class 10?**

three important

Ans: There are three important formulas in coordinate geometry studied in Class 10.

### What is the formula of triangle in coordinate geometry?

The formula of area of triangle formula in coordinate geometry the area of triangle in coordinate geometry is: A = (1/2) |x1 1 (y2 2 − y3 3 ) + x2 2 (y3 3 − y1 1 ) + x3 3 (y1 1 − y2 2 )|, where (x1 1 ,y1 1 ),(x2 2 ,y2 2 ), and (x3 3 ,y3 3 ) are the coordinates of vertices of triangle.

**What is the distance formula in coordinate geometry?**

Distance can be calculated using the formula derived from Pythagoras theorem. In coordinate geometry, the distance formula is √[(x2 – x1)^2 + (y2 – y1)^2].

#### What is the vector formula?

the formula to determine the magnitude of a vector (in two dimensional space) v = (x, y) is: |v| =√(x2 + y2). This formula is derived from the Pythagorean theorem. the formula to determine the magnitude of a vector (in three dimensional space) V = (x, y, z) is: |V| = √(x2 + y2 + z2)

**What are the formulas for triangles?**

These triangle formulas can be mathematically expressed as;

- Area of triangle, A = [(½) b × h]; where ‘b’ is the base of the triangle and ‘h’ is the height of the triangle.
- Perimeter of a triangle, P = (a + b + c); where ‘a’, ‘b’, and ‘c’ are the 3 sides of the triangle.

## Where is section formula used?

Section formula is used to determine the coordinate of a point that divides a line segment joining two points into two parts such that the ratio of their length is m:n.

**What is the formula of area of ∆ ABC?**

For example, In ∆ABC, when sides ‘b’ and ‘c’ and included angle A is known, the area of the triangle is calculated with the help of the formula: 1/2 × b × c × sin(A).

### What is the formula of area of quadrilateral in coordinate geometry?

Area of quadrilateral = (½) × diagonal length × sum of the length of the perpendiculars drawn from the remaining two vertices.

**What is the formula of time?**

To solve for time use the formula for time, t = d/s which means time equals distance divided by speed.

#### What is matrix formula?

A matrix equation is an equation of the form Ax = b , where A is an m × n matrix, b is a vector in R m , and x is a vector whose coefficients x 1 , x 2 ,…, x n are unknown.

**What are the 3 formulas for the area of a triangle?**

Area of triangle = 1/2 × side 1 × side 2 × sin(θ); when 2 sides and the included angle is known, where θ is the angle between the given two sides. Area of an equilateral triangle = (√3)/4 × side. Area of an isosceles triangle = 1/4 × b√4a2−b2 4 a 2 − b 2 ; where ‘b’ is the base and ‘a’ is the length of an equal side.

## Where is midpoint formula used?

Midpoint formula is used to find the centre point of a straight line. Sometimes you will need to find the number that is half of two particular numbers. For that, you find the average of the two numbers.

**What is section formula and midpoint formula?**

Section formula for external division is: P(x, y) = (mx2−nx1m−n,my2−ny1m−n) ( m x 2 − n x 1 m − n , m y 2 − n y 1 m − n ) Midpoint formula is: M(x, y) = (x2+x12,y2+y12) ( x 2 + x 1 2 , y 2 + y 1 2 )

### What is r in triangle?

The area of the triangle is represented by Δ. R represents the radius of the circum-circle and r represents the radius of the in-circle. We know, ∠BCA + ∠ABC + ∠BAC = Π or C + B + A = Π

**What is the formula of rhombus?**

d1 = length of diagonal 1. d2 = length of diagonal 2. b = length of any side. h = height of rhombus….Area of Rhombus Formula.

Formulas to Calculate Area of Rhombus | |
---|---|

Using Base and Height | A = b × h |

Using Trigonometry | A = b2 × Sin(a) |

#### What is the formula of area of polygon?

Area of Polygon Formulas

Name of the Polygon | Area Formula |
---|---|

Triangle | 1/2 × base × height |

Square | side2 |

Rectangle | length × width |

Pentagon | 5/2 × side length × distance from the center of sides to the center of pentagon |

**What are some examples of geometry formulas?**

Geometry formulas are used in maths to find the perimeter and area of plane figures, surface area and volume of three-dimensional shapes. Example 1: Calculate the area of a trapezium with parallel sides of 24 c m and 20 c m and a distance of 15 c m between them. Solution: Given the length of parallel sides 24 c m and 20 c m, and the distance

## How do I prove the midpoint theorem using coordinate geometry?

Proof: Using the midpoint formula , the coordinates of the midpoints X and Y are. X ( 0 + b 2, 0 + c 2) = X ( b 2, c 2) Y ( a + b 2, 0 + c 2) = Y ( a + b 2, c 2) First note that the slope is 0 , since. m = rise run = ( c 2 − c 2) ( b 2 − ( a + b 2)) = 0 ( b 2 − ( a + b 2)) = 0. So, X Y ¯ is parallel to P R ¯ .

**How to solve coordinate geometry problems?**

The sequence of the chapter to be followed: Straight Lines,Circles,Parabola,Ellipse,and Hyperbola.

### How do you prove a right angle using coordinate geometry?

Proof of Right Angle Triangle Theorem. Theorem:In a triangle, if square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle. To prove: ∠B = 90 ° Proof: We have a Δ ABC in which AC 2 = A B 2 + BC 2. We need to prove that ∠B = 90 ° In order to prove the above, we