Place a smaller page on a larger one. How many corners are you able to match with each other?
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Practice makes perfect
To explain why one point will be on the same place we will demonstrate an example. Here is an example page given the width and the height.
We have a page with width 20 cm and height 30 cm. When doing a reduction the scale factor is k<1. Therefore, we will choose the scale factor k= 12 to dilate the original page. Since multiplying something by 12 is the same as dividing by 2 we will divide the width and height by 2.
Width:& 20 2=10cm, Height: 30 2=15
Now that we have the width and height of the dilated page, we can place it on top of the original one.
We can now see the dilated page above the original page. The lower left corner is at the same position for the two pages. Let's name the corners of the original paper to ABCD and the dilated pages corners to A'B'C'D'. The position of A and A' will then be the same.
Since no center was declared, we assumed that the center of dilation was the origin. In this case, that would be point A(0,0). When we multiply the coordinates by the scale factor, we get the same coordinates due to the Multiplicative Property of Zero.
