"Changing Fish" Position and Coordinates PPT Courseware

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"Changing Fish" Position and Coordinates PPT Courseware

In the plane Cartesian coordinate system, trace the following points and connect these points with line segments in turn. The coordinates of the points are

(0,0), (5,4), (3,0), (5,1),

(5,-1), (3,0), (4,-2), (0,0).

Can you understand the meaning of sequential connection?

What kind of graph did you get?

Exploration of new knowledge—translation of graphics

1. Place each "vertex" of the fish in the above exercise (0,0), (5,4), (3,0), (5,1), (5,-1), (3,0), The ordinates of (4, -2) and (0, 0) remain unchanged, add 3 to the abscissas respectively, and then connect the obtained points with line segments. What changes does the resulting pattern have compared with the original pattern?

2. Place the "vertexes" of the fish in the above exercise (0,0), (5,4), (3,0), (5,1), (5,-1), (3,0), The ordinates of (4, -2) and (0, 0) remain unchanged, and the abscissas are added to -2 respectively. Then the obtained points are connected in sequence with line segments. What changes does the resulting pattern have compared with the original pattern?

3. Place the "vertexes" of the fish in the above exercise (0,0), (5,4), (3,0), (5,1), (5,-1), (3,0), The abscissa coordinates of (4, -2) and (0, 0) remain unchanged, and the ordinate coordinates are added by 3 respectively. Then the obtained points are connected in sequence with line segments. What changes does the resulting pattern have compared with the original pattern?

4. Place the "vertexes" of the fish in the above exercise (0,0), (5,4), (3,0), (5,1), (5,-1), (3,0), The abscissa coordinates of (4, -2) and (0, 0) are +2 respectively, and the vertical coordinates are added 3 respectively. Then connect the obtained points with line segments in sequence. What changes does the resulting pattern have compared with the original pattern?

Summarize

translation transformation

1. When the ordinate remains unchanged and the abscissa increases (decreases) by a unit respectively, the graph will translate a unit to the right (left) along the X-axis;

2. When the abscissa remains unchanged and the ordinate increases (decreases) by a unit respectively, the graph translates upward (downward) by a unit along the Y-axis;

scale transformation

1. The ordinate remains unchanged, the abscissa becomes a times the original value respectively, the graph is laterally extended to be a times the original value (a>1) or the graph is shortened laterally to a times the original value (0

2. The abscissa remains unchanged, the ordinate becomes a times the original value respectively, the graph is lengthened vertically to a times the original value (a>1) or the graph is shortened vertically to a times the original value (0

Consolidation exercises

1) If 3 units are added to the abscissa of each point of a graph (the ordinate remains unchanged), the graph will translate ___ units toward ___.

2) If the abscissa of each point of a graph is subtracted by 5 units (the ordinate remains unchanged), the graph will translate ___ units toward ___.

3) If 2 units are added to the ordinate of each point of a graph (the abscissa remains unchanged), the graph will translate ___ units toward ___.

4) If 6 units are subtracted from the ordinate of each point of a graph (the abscissa remains unchanged), the graph will translate ___ units toward ___.

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Update Time: 2024-07-31

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