# Moving in the Plane

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

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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.

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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.â€‹
• Check “Show image”. The Source and the image are at the same location since the angle is zero degrees.â€‹
• Now, check “Show center” to locate a center of rotation outside the figure.â€‹
• 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.

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(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.