Analytic Geometry: Graphic Solutions Using Matlab Language

CONTENTS

PREFACE

SEGMENTS

DISTANCE BETHWEEN POINTS

VECTORS

STRAIGTH LINE SLOPE

STRAIGTH LINE

CIRCUMFERENCE

ELLIPSE

PARABOL

HIPERBOLE

ROOT LOCUS PROBLEMS

GRAPHIC AND EMPIRIC EQUATIONS

POLAR EQUATIONS

PARAMETRIC EQUATIONS

BIBLIOGRAPHY

PREFACE

FOR THE SOLUTON OF THE PROBLEMS THIS BOOK INCLUDE ARE: THE COMMONLY SOLUTION USED IN THE ANALYTIC GEOMETRY SUBJET, AND THE GRAPHIC SOLUTIONS USING MATLAB LANGUAGE WITH THE PURPOSE HELP AT THE STUDENT VISUALIZE AND LEARN COMPUTER PROGRAMMING.

SEGMENTS

PROBLEM 1. DRAW THE POINTS A(4,4), B(-4,4), C(-4,-4), D(4, -4) AND E(2^.5, 3^.5).

x = -4: .001: 4;

if (16 - x.*x) >= 0

y = sqrt(16 - x.*x);

end

if (16 - x.*x) >= 0

y1 = - sqrt(16 - x.*x);

end

x = -4: .001: 4;

y2 = ((3/2)^.5)*x;

x = -4: .001: 4;

y3 = -4;

x = -4: .001: 4;

y4 = 4;

plot(x,y, x, y1, x, y2, x,y3, x, y4);

xlabel(‘X’);

ylabel(‘Y’);

title(‘CIRCLE ‘);

PROBLEM 2. WHICH ARE THE ALGEBRAIC SIGNS OF THE COORDINATES IN EACH OF THE FOUR QUADRANTS?

QUADRANT I (+, +)

QUADRANT II (-, +)

QUADRANT III (-,-)

QUADRANT IV (+,-)

PROBLEM 3. IF ONE POINT IS OVER X AXLE, WHAT IS ITS ORDINATE? IF THE POINT IS OVER Y AXLE, WHAT IS IT’S ABSCISE? WHERE ARE SITUATED THE POINTS WHOSE ABSICE IS X = 1? AND WHERE THE POINTS HAVE Y = -2?.

a) y = 0;

b) x = 0;

c) OVER Y AXLE.

d) OVER X AXLE.

PROBLEM 4. DRAW THE POINTS A (0, -2), B (1, 1), C (2, 4) AND D (-1,-5) AND PROBE THAT THE POINTS ARE OVER A STRAIGTH LINE.

mAB = (1 + 2)/(1 – 0) = 3,     mCD = (-5 – 4)/(-1- 2) = (-9/-3) = 3

x = -1: .001: 2;

%(y- y1) = m(x - x1)

y = (3)*x +2;

plot(x,y);

xlabel(‘X’);

ylabel(‘Y’);

title(‘STRAIGTH LINE ‘);

PROBLEM 5. PROBE GRAPHYCALLY THAT THE NEXT POINTS ARE SITUATED OVER ONE CIRCLE AND FIND ITS CENTER AND RADIUS.

x = -5: .001: 5;

if (25 - x.*x) >= 0

y = sqrt(25 - x.*x);

end

if (25 - x.*x) >= 0

y1 = -sqrt(25 - x.*x);

end

plot(x,y, x, y1);

xlabel(‘X’);

ylabel(‘Y’);

title(‘CIRCLE OF RADIUS 5’);

PROBLEM 6. DRAW THE POINTS A (1, 2) AND B (3, 4). SUPPOSE THAT THE HORIZONTAL BY POINT A INTERSECT THE VERTICAL BY POINT B IN P. WHAT ARE THE COORDINATES OF POINT P? WHISH ARE THE LONGITUDE OF AP AND BP? CALCULATE THE DISTANCE AB

a) P (1,4) LONGITUDE AP = X2 –x1 = 0; y2 –y1 = 2; AP = 2 BP = x2-x1 = 2, y2 –y1 = 0;

BP = 2     DISTANCE AB = ((x2-x1)^2 + (y2-y1)^2)^.5 = (4 + 4)^.5 = 2(2)^.5

PROBLEM 7. FIND THE DISTANCE BETWEEN A (-2,-2) AND B (3, -4).

AB = ((-2 -3)^2+ (-2 +4)^2)^.5 = (25 + 4)^.5 = (29)^.5

DISTANCE BETHWEEN POINTS

PROBLEM 1. FIND PERIMETER OF THE TRIANGLE FORMED BY THE POINTS A (2, 3),

B(-3,3) AND