Translations

First we need to draw a triangle and select its interior.

• To select the interior, highlight the vertices of the triangle that you have drawn and under the CONSTRUCT menu select TRIANGLE INTERIOR.

Triangle with interior selected

• Now we must draw a translation vector.
  • Draw a segment and select both of its endpoints.
  • Under the TRANSFORM menu, select MARK VECTOR.
Translation Vector

 

• Highlight your triangle by highlighting the vertices, sides, and the interior of you triangle.
  • Under the TRANSFORM menu, select TRANSLATE.
  • Then select BY MARKED VECTOR.

   

  Translation of the triangle

• Now let us see what happens if we move the vertices of the original triangle.

Moving point A
Moving point B
Moving point C

• Lets move the translation vector to where it hits the vertices and edges of the triangle. What do you notice?
  • Based on your observations, can you tell what the translation vector does to the new image of the triangle?

Moving vector to an edge
Moving vector to point A
Moving vector to point B
Moving vector to point C

You should notice that the translation vector is connects to the corresponding point on the reflected image.

• Now see what happens if you had moved the endpoints of your translation vector.

Moving endpoints of segment

• Now let us connect the corresponding vertices of both triangles and see what happens. Measure the length of the connecting segments.
  • To measure the length select the line that you want to measure.
  • Under the MEASURE menu, select length.
  • Do this for all the segments and the translation vector. What do you notice?

Connecting the vertices with measures

This should confirm to you that the translation vector is the amount that the corresponding point on the original image moves away.

Other Translations

• Now let us create a new sketch.
• Go to the GRAPH menu and select GRID FORM and then select POLAR GRID.
• Construct a triangle.

Vector and triangle in polar grid

• Now select the vertices, edges, and the interior of the triangle.
  • Under the Transform menu, select TRANSLATE.
    • Make sure that POLAR is selected.
    • Make sure that FIXED DISTANCE is selected.
      • Put in a fixed distance.

A fixed distance of 1 cm.

• Connect the vertices and put in measurements for the segments.
• Play with the vertices. Move them around. What do you notice?

Connecting points with measures
Moving point A
Movng point B
Movng point C

You should notice that no matter which way that you move the points on the original image, the translated image will continue to be that fixed distance that you put in away from its corresponding poinnt.

Rotations

Reflections

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