COORDINATE GEOMETRY
by SONIA LAGUNDAON
1. WRITING THE EQUATIONS OF THE LINE
1.1. linear equations can be written in 3 forms
1.1.1. Standard Form : Ax + By = C
1.1.2. General Form : Ax + By + C = 0
1.1.3. Slope - Intercept Form : y = mx + b
2. GRAPHING LINEAR EQUATIONS
2.1. we can graph linear equations using
2.1.1. x - and y intercepts
2.1.2. a point and slope of the line
2.1.3. two points of the line
3. PARALLEL AND PERPENDICULAR LINES
3.1. Two lines are parallel if they have the same slope and different y - intercepts
3.1.1. slope of L1 = slope L2
3.2. Two lines are perpendicular if their slopes are opposite reciprocals
3.2.1. the product of their slopes is always equal to -1
4. EQUATION OF THE CIRLE
4.1. In mathematics , CIRCLE is defined as the set of all points equidistant from a fixed point called center
4.2. The center C is at (h, k), r is the radius and P(x, y) is a point on the circle.
4.3. the distance formula is used to find the equation of the circle
4.3.1. thus the equation of the circle whose center is at (h, k) and with radius r is
5. THE DISTANCE FORMULA
5.1. it is used to find the distance between two points on the coordinate plane
5.2. Pythagorean Theorem can be used to find the distance between two points.
5.2.1. The Pythagorean theorem is attributed to Greek mathematician PYTHAGORAS OF SAMOS
6. MIDPOINT FORMULA
6.1. the midpoint of a segment is a point that divides the segment into two congruent segments
6.2. to find the midpoint of a line, simply find the x and y coordinates of the midpoint
6.3. to find the x coordinates
6.3.1. add the first and second value of x and divide it by two
6.4. to find the y coordinates
6.4.1. add the first and second value of y and divide it by two