# analytical geometry calculating the shortest distance between a point and a line 1 part 1

##
Introduction to Analytic **Geometry**

Lesson#**1**

Introduction to **Analytical** **Geometry**

Rene Descartes (1596-1650), French, (Father of Modern Philosophy)

Writing exponents as…

##
What is **distance** ? **Distance** formula

Lesson#6

What is **distance** ? **Distance** formula

What is **Distance**?

Length of **shortest** path **between** two points.

OR

Length…

## Classification of Quadrilateral (3)

Lesson#21

Classification of Quadrilateral (3)

Isosceles Trapezium: ** A** quadrilateral having equal diagonals is called an isosceles…

##
Classification of Quadrilateral (**1**)

**1**

Lesson#19

Classification of Quadrilateral (** 1**)

Quadrilateral or Tetragon or Quadrangle

**ploygon having four sides or four vertices…**

**A**## Classification of Quadrilateral (2)

Lesson#20

Classification of Quadrilateral (2)

TRAPEZIUM: ** A** quadrilateral having at-least one pair of parallel sides. It is called…

##
Circles connected with **a** Triangle (**1**)

**a**

**1**

Lesson#24

Circles connected with ** a** Triangle (

**)**

**1**CIRCLES CONNECTED WITH

**TRIANGLE**

**A**Introduction to

**Analytical**

**Geometry**

## Question No .17 , Question No .16

Lesson#28

Question No .17

Q.17. **The** points (4,-2), (-2,4) **and** (5,5) are **the** vertices of ** a** triangle. Find in-center of

**the**triangle.

##
Prove that Bisectors of angles of **a** triangle are concurrent

**a**

Lesson#27

Prove that Bisectors of angles of ** a** triangle are concurrent.

THEOREM: Bisectors of angles of

**triangle are concurrent.**

**a**## Lesson#17 [ Classification of Triangle, Question No . 4 ]

Lesson#17

Classification of Triangle

Question No . 4

Triangle or Trilateral or Trigon

Classification by Sides: Scalene…

## Question No.11

Lesson#23

Question No.11

Find h such that **the** quadrilateral with vertices ** A**(-3,0), B(

**,-2), C(5,0)**

**1****and**D(

**,h) is parallelogram, Is it…**

**1**## Theorem related to Centroid

Lesson#26

Theorem related to Centroid

THEOREM: **The** centroid of ** a** ^ABC is

**a****point**that divides each median in

**the**ratio 2:

**. Using this…**

**1**##
Circles connected with **a** Triangle (2)

**a**

Lesson#25

Circles connected with ** a** Triangle (2)

EX-CIRCLE or E-CIRCLE or ESCRIBED CIRCLE, E-CENTER

Some other definitions…

## Question No.10, Question No 4(iii)

Lesson#22

Question No.10

Q.10. ** A** quadrilateral has

**the**points

**(9,3), B(-7,7), C(-3,-7),**

**A****and**D(5,-5) as its vertices. Find

**the**midpoints…

## Lesson#18 [ Question No.6 , Question No.9, Question No.12 ]

Lesson#18

Question No.6

Q.6. Find h such that **the** points ** A**(3,-

**), B(0,2)**

**1****and**C(h,-2) are vertlees of

**right triangle with right angle at…**

**a**## Question No. 5

Lesson#12

Question No.5

Q.5. **The** midpoints of **the** sides of ** a** triangle are (

**,-**

**1****), (-4,-3)**

**1****and**(-

**,**

**1****1**). Find coordinates of

**the**vertices…

## Question No. 3 ,Question No. 8

Lesson#11

Question No. 3

Question No. 8

Q.3. which of **the** following points are at **a****distance** of 15 units from **the** origin?

## How to check that points are collinear ?

Lesson#15

How to check that points are collinear ?

What are col-linear points?

points are said to be col-linear if they lie on ** a**…