Using GeoGebra in Analitic geometry

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Using GeoGebra in Analitic geometry

• Svetlana Maletin
• Verica Govedarica
• High school "Jovan Jovanovic Zmaj"
• Novi Sad, Serbia

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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.
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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 ( k2k1 )

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Line.

• x/m y/n 1
• perpendicular lines
• y k x n1
• y -1/k n2
• ( k2 -1/k1 )

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A lot of tasks...
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Circle.

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

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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

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Intersection of circle and line.

• tangents on c perpendicular to a fixed line

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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

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Ellipse.

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

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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

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Ellipse.

• Moving point M?c, dd1d2 const.
• equation

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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

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Hyperbola. Equation. Asymptote.

• Equation
• Asymptote of hyperbla

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Parabola.

• equation y2 2 p x
• focus F( p/2, 0)
• directrix x - p/2

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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,
  the students 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.

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Test. Results of group A

• Group A learned Analitic Geometry on the clasic
  way, without using GeoGebra.

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Test. Results of group B

• Group B learned Analitic Geometry using GeoGebra.

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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