# COORDINATE GEOMETRY

# COORDINATE GEOMETRY

by SONIA LAGUNDAON
# 1. THE DISTANCE FORMULA

## 1.1. it is used to find the distance between two points on the coordinate plane

## 1.2. Pythagorean Theorem can be used to find the distance between two points.

### 1.2.1. The Pythagorean theorem is attributed to Greek mathematician PYTHAGORAS OF SAMOS

# 2. MIDPOINT FORMULA

## 2.1. the midpoint of a segment is a point that divides the segment into two congruent segments

## 2.2. to find the midpoint of a line, simply find the x and y coordinates of the midpoint

## 2.3. to find the x coordinates

### 2.3.1. add the first and second value of x and divide it by two

## 2.4. to find the y coordinates

### 2.4.1. add the first and second value of y and divide it by two

# 3. WRITING THE EQUATIONS OF THE LINE

## 3.1. linear equations can be written in 3 forms

### 3.1.1. Standard Form : Ax + By = C

### 3.1.2. General Form : Ax + By + C = 0

### 3.1.3. Slope - Intercept Form : y = mx + b

# 4. GRAPHING LINEAR EQUATIONS

## 4.1. we can graph linear equations using

### 4.1.1. x - and y intercepts

### 4.1.2. a point and slope of the line

### 4.1.3. two points of the line

# 5. PARALLEL AND PERPENDICULAR LINES

## 5.1. Two lines are parallel if they have the same slope and different y - intercepts

### 5.1.1. slope of L1 = slope L2

## 5.2. Two lines are perpendicular if their slopes are opposite reciprocals

### 5.2.1. the product of their slopes is always equal to -1

# 6. THE SHORTEST DISTANCE BETWEEN A POINT AND A LINE

## 6.1. the shortest distance is the one drawn perpendicular to the line.

# 7. EQUATION OF THE CIRLE

## 7.1. In mathematics , CIRCLE is defined as the set of all points equidistant from a fixed point called center

## 7.2. The center C is at (h, k), r is the radius and P(x, y) is a point on the circle.

## 7.3. the distance formula is used to find the equation of the circle

### 7.3.1. thus the equation of the circle whose center is at (h, k) and with radius r is

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