analytic geom and distance formula

Prepared 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.

Prepared by:

Mr. Raymond B. Canlapan

THE CARTESIAN PLANE

Define the following:

x-axisy-axisOriginQuadrantsOrdered pairAbscissaOrdinate

REVIEW: PLOT (3, -4)

Prepared by:

Mr. Raymond B. Canlapan

What is the distance between the two points?

Remember:

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)

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.