Moving in the Plane

Investigate Translation on a Coordinate System.

  • Drag the X in the diagram below, to the point (3, 0) and note the new position of the triangle. ​
  • Drag X to the point (-3, 0) and note the new position of the triangle. ​
  • Drag X to the point (0, 3) and note the new position of the triangle. ​
  • Drag X to the point (0, -3) and note the new position of the triangle. ​
  • Drag X to other locations on the plane and note the horizontal and vertical displacements of each pair of corresponding points on the triangles.

Investigate Reflection on a coordinate system.

(A). Grab a point on the triangle on the left (original figure) and move it around.

(B). Check each box in the figure below and answer the question that describes the reflection. Off-screen images can be brought in by pan and zoom.

Investigate Rotation on a Coordinate System.

(A). Click on the slider and move it to the right to see a rotation about a center within the figure.

(B). Locate center of rotation.

  • Check the “Show original” box for the source image.​
  • Check “Show image”. The Source and the image are at the same location since the angle is zero degrees.​
  • Now, check “Show center” to locate a center of rotation outside the figure.​
  • Move the slider to see how a rotation occurs about a point not within the figure.

(C). Use the line tool to connect A and A’, B and B’, C and C’ . Note the point of intersection of all the lines.

(1). If you connect the points in the applet above, do they form an equilateral triangle? How can you prove it?

(2). If it is not an equilateral triangle, add another point D in a place that would make an equilateral triangle.