Coordinate Moves

Move LARGE POINTS on the triangle around to see the effect of translation on Lisa’s picture. The original picture has coordinates at the base.

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Applications of Transformations on Plane Figures.

Five points are plotted on the coordinate plane below.

  • Using the Pen tool   or the Text tool, label each of its coordinates.​
  • Using the x-axis as the line of reflection, plot the image of each point.​
  • Label the image of each point with its coordinates.​
  • Include a label using a letter. For example, the image of point A should be labeled A’.​

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Apply transformations to a line segment.

Apply each of the following transformations to segment AB using the applet that follows. Use the Pen tool to record the coordinates.

  • In the applet below, rotate segment AB 90 degrees counterclockwise around center B by moving the slider marked 0 degrees. The image of B is named C .
  • In the applet below, rotate segment AB 90 degrees counterclockwise around center A by moving the slider marked 0 degrees. The image of B is named D .
  • In the applet below, rotate segment AB 90 degrees counterclockwise about (0, 0) by moving the slider marked 0 degrees. The image of A is named E and the image of B is named F .

Compare the two 90-degree counterclockwise rotations of segment  AB.

(1). What is the same about the images of these rotations?

(2). What is different about the images of these rotations?

(3). Suppose EF and GF are line segments of the same length. Describe a sequence of transformations that moves EF to GF.

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More Applications of Transformation on Plane Figures.

(A). Here are some points below. Translate the points to the right by 4 units and up by 1 unit. Plot these points on the grid, and label them A’, B’, and C’.

(B). Here are some points below. Reflect the points over the – axis. Plot these points on the grid, and label them D’, E’, and F’.

(C). Here are some points below. Rotate the points about (0, 0) by 90 degrees clockwise. Plot these points on the grid, and label them G’, H’, and I’.

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The point R has coordinates (3, 2).

  • Without graphing, predict the coordinates of the image of point R  if it were reflected using the x–axis as the line of reflection.​
  • Check your answer by finding the image of R on the graph.​
  • Label the image of R as I

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If the point (13, 10) were reflected using the – axis, as the line of reflection, what would be coordinates of the image?

What would be the coordinates of the points (13, -20), (13, 570). Explain how you know in each case.

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