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Using GeoGebra in Analitic geometry

Using GeoGebra in Analitic geometry. Svetlana Maletin Verica Govedarica High school "Jovan Jovanovic Zmaj" Novi Sad, Serbia. Two views: the algebra window and the geometry window an expression in the algebra window corresponds to an object in the geometry window and vice versa . Line.

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Using GeoGebra in Analitic geometry

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  1. Using GeoGebra in Analitic geometry Svetlana Maletin Verica Govedarica High school "Jovan Jovanovic Zmaj" Novi Sad, Serbia

  2. Two views: the algebra window and the geometry windowan expression in the algebra window corresponds to an object in the geometry window and vice versa.

  3. Line. • y = k x • discuss: how the parameter k influeces the direction of line • y = k x + n • discuss how the parameter n influences the y-axis segment • parallel lines ( k2=k1 )

  4. Line. • x/m + y/n =1 • perpendicular lines • y = k x + n1 • y = -1/k + n2 ( k2 = -1/k1 )

  5. A lot of tasks...

  6. Circle. • Circle c(O,r) • center: point C(p,q) • radius: r • ----------------------- • equation: • (x-p)2 + (y-q)2 = r2

  7. Intersection of circle and line. • Intersection of circle c(O,r) and line y = k x + n for diferent k and n • tangents to circle paralel with fixed line

  8. Intersection of circle and line. • tangents on c perpendicular to a fixed line

  9. Intersection of circle and line. • tangents through point Mc on c, for diferent place of point M • tangent through point Ac on c, for diferent place of point A on c

  10. Ellipse. • major axis = 2a, minor axis = 2b • a is semimajor axis, b is semiminor axis • circle is a special case of an ellipse

  11. Ellipse. • ellipse - the locus of points on a plane where the sum of the distances from any point on the curve to two fixed points is constant. • The two fixed points are called foci (plural of focus). • F1(-c,0), F2(c,0) c2 = a2 - b2

  12. Ellipse. • Moving point Mc,d=d1+d2= const. • equation:

  13. Hyperbola. • Hiperbola - the locus of points on a plane where the difference of the distances from any point on the curve to the two fixed points is constant. • The two fixed points are called foci (plural of focus). • F1(-c,0), F2(c,0) c2 = a2 + b2

  14. Hyperbola. Equation. Asymptote. • Equation: • Asymptote of hyperbla

  15. Parabola. • equation: y2 = 2 p x • focus: F( p/2, 0) • directrix: x = - p/2

  16. Reasons for introduction GeoGebra into teaching • GeoGebra is a simple and interesting tools suitable for teaching Analitic geometry. • Using the algebra window and the geometry window, thestudents get a clear view of the things that they are learning. • GeoGebra is especially usefull for the first encounter with conics. • GeoGebra is helpfull to teachers for making a lot of tasks with ease.

  17. Test. Results of group A • Group A learned Analitic Geometry on the clasic way, without using GeoGebra.

  18. Test. Results of group B • Group B learned Analitic Geometry using GeoGebra.

  19. Problems with using GeoGebra in teaching • Problems may occur when working with large groups of students, because of some of them can't concentrate. • GeoGebra can't be used allone, becase the students must learn to use equations and finsh tasks by themselves

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