analytic geom and distance formula

THE STUDY OF ANALYTIC

GEOMETRYPrepared by:

Mr. Raymond B. Canlapan

FLIES

ANALYTIC GEOMETRY: DEFINITION AND HISTORYIt is the merging of two branches of Mathematics—algebra and geometry—into a single, unified body of knowledge.

ANALYTIC GEOMETRY: DEFINITION AND HISTORYIt is one of the great achievements in

mathematics that occurred in the early 1600s.

Credit for this great accomplishment goes to the French mathematician Rene Descartes.

The same method was also discovered by another famous French mathematician Pierre de Fermat.

REVIEW OF CARTESIAN COORDINATE SYSTEM

Prepared by:

Mr. Raymond B. Canlapan

THE CARTESIAN PLANE

Define the following:

x-axisy-axisOriginQuadrantsOrdered pairAbscissaOrdinate

REVIEW: PLOT (3, -4)

THE DISTANCE FORMULA

Prepared by:

Mr. Raymond B. Canlapan

What is the distance between the two points?

Remember: The distance between any two

points is computed by the formula

Example 1:

Find the distance between P (0, 1) and Q (3, 5).

Example 1:

Find the distance between P (2, -2) and Q (6, 1).

Example 2:

Find the distance between P (-2, -2) and Q (6, 4).

Example 3:

Find the distance between P (3, 1) and Q (0, -2).

Seatwork: Find the distance between the following points:

(5, -4) and (5, 4) (10, -1) and (-2, -4) (1, 5) and (7, 5) (-1, -1) and (-2, -2)

APPLICATION OF DISTANCE FORMULA

Prepared by:

Mr. Raymond B. Canlapan

PRE-REQUISITE CONCEPTS:Collinear Points -- The points A,

B, and C are collinear, with B between A and C, if and only if

AB + BC = AC.

A B C

PRE-REQUISITE CONCEPTS:

Triangle – a polygon of three sides. It can be:

Equilateral – when all sides are equal

Isosceles – when two sides (legs) are equal

Scalene – when no sides equal

EXAMPLE # 1:

Points D (1, 3), E (-1, -1), and F (-3, -2) are in a plane. Are these collinear?

EXAMPLE # 2:

The following are the coordinates of the three points which are the vertices of a triangle: (8, -3), (-3, 4), and (6, 6). Is the triangle equilateral, isosceles or scalene?

EXAMPLE # 3:

The vertices of a triangle are at E (4, 0), F (2, 1), and G (-1, -5). What kind of triangle is it?

Seatwork:

1. Plot the points (0, 0), (-3, -3) and (4, 4) and state whether they are collinear or not.

2. Show that the points A (2, 6), B (-3, -3) and C (6, 2) are vertices of an isosceles triangle.