FUNCTIONS AND GRAPHS II

Representation of Points

Locating points with integer coordinate values.

1.- Locate and write on your notebook the coordinates of the points A, B, C, D, E, F and G. (Move the red dot and locate it over each of the points to find out their coordinates)

Locating points with decimal coordinate values.

2.- Locate and write on your notebook the coordinates of the points A, B, C, D, E, F and G. (Write down on the text fields named  abscissa and ordinate the values you can guess and afterwards use the arrows to move the red dot and place it over the yellow points so they hide under the red dot.)

Calculating coordinates

3.- If a square ABCD has two consecutive points on A (2,3) and B (7,3) ,  which will the coordinates of the other two point C(x1,y1) and D(x2,y2) be?

How many solutions can you find?

Calculating coordinates

4.- If two consecutive vertices of the square ABCD are A (3,2) and B (-1,2)  where may the other two C(x1,y1) and D(x2,y2) be?

Symmetries

5.- Construct a table, on your notebook, with the coordinates of the points which are symmetric to the given ones with respect to the X axis, with respect to the Y axis and with respect to the origin, respectively. Analyse your results and describe the relations existing between the coordinates of the symmetric points.

Symmetric Figures

6.- Drag the red point and observe that the symmetric points describe symmetric figures. (Use the clear button or the secondary mouse button to erase the trace left by the points.)

Coordinates of the points on a horizontal line

7.- Write on your notebook the coordinates of several points that are on the same horizontal line.  What do their coordinates have in common? (Use the Clear button or the secondary mouse button to erase the trace left by the red dot.)

What can you say of the coordinates of the horizontal line passing through the point  (1 , -2.6)?

Try with different lines and write on your notebook your conclusions.

Points with equal coordinates.

8.- Observe the points for which both coordinate have the same value. What kind of curve do these points form?

For all these points the ordinate and the abscissa are equal to each other, in other words:

y = x

Author: Juan Madrigal Muga

	Ministerio de Educación, Cultura y Deporte. Año 2000