GeoGebra Classroom

# Photocopy Faux Pas

In the applet below we see what Burnell did to the original picture to be enlarged. Notice that the original picture is in the center of the paper to be photocopied and the enlargement is set to 200% (Scale Factor of 2). Follow the steps below and use your findings to answer the questions at the end of this activity. Step 1: Using the "line" tool, construct a line that connects corresponding points A and A'. Use the point tool to place a point where the line touches the top left corner of the paper label this point O. What do you think this point is? Step 2: Use the measure tool to measure the distance from point O (top left corner) to point B. Use a calculator to double this length for a dilation with scale factor 2. Step 3: Use the "Segment with given length" tool to construct a line segment at point O, that has a length equal to twice the length of OB. Label the new endpoint B'. Use the move tool to drag B' so that the segment intersects the original point B. You have now dilated point B by a factor of 2, centered at point O. Step 4: Repeat Step 2 and 3 for the remaining points C and D to construct segments twice the length of OC and OD. Name the new segments OC' and OD', respectively, and align so that the segments intersect the original points C and D. Step 5: You should now have four points: A', B', C', D' that were constructed by doubling the length from the point of dilation to points on the pre-image. Use the polygon tool to construct quadrilateral A'B'C'D'.

Explain how the photocopy machine produced the partial copy of the original picture (pre-image).

Where should Burnell have placed the original picture to ensure that the enlarged image would be centered on the paper?

Mr. Donahue complained that the enlarged image was four times as big as the original image. What do you think? Did Burnell double or quadruple the original image? What evidence do you give to support your claim?

Enlarging a pre-image is a transformation called a dilation. Using your experience with this task, what are some defining features of a dilation?