Analytic Geometry: Graphic Solutions Using Matlab Language
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About this ebook
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.
Related to Analytic Geometry
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Book preview
Analytic Geometry - Ing. Mario Castillo
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).
Image9116.jpgx = -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 ‘);
Image9129.jpgPROBLEM 5. PROBE GRAPHYCALLY THAT THE NEXT POINTS ARE SITUATED OVER ONE CIRCLE AND FIND ITS CENTER AND RADIUS.
Image9137.jpgx = -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