ANALYTIC GEOMETRYMATH 004

Lecture #3

• Area of a polygon given coordinate points

• Straight line1. Equations of a line

a. Standard equationsb. General equation

AREA OF A POLYGON GIVEN COORDINATE POINTS

The area of a polygon given coordinate points is given by the determinants

or

Sample Problem

1. Determine the area of the triangle with vertices at:

a. b. c. d.

STRAIGHT LINE: EQUATIONS OF A LINE

Standard equations of a linea. SLOPE-POINT FORM – the slope point form

is given by the equation

b. SLOPE-INTERCEPT FORM – the slope intercept form is given by the equation

c. INTERCEPT FORM - the intercept form is given by the equation

d. TWO-POINT FORM - the two point form equation of the line is given by

The general form of the equation of a line is given by

where A, B and C are non-zero constants and x

and y are variables of degree one.

Sample Problem1. Find the general equation of the line through with

slope 4.2. Find the general equation of the line passes through

the point and .3. Find the general equation of the line having gradient

of and y-intercept of .4. Reduce the equation of to the slope intercept form.

5. Find the general equation of the line having x-intercept of 3 and y-intercept of -2.6. Find the general equation of the line passes through the point and with equal intercepts.7. Determine the general equation of the line passes through the following points:

a. b.