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Enlargement (or Dilation) with a great app

March11

There is a good app from waldomaths (Java required) to see what happens when we have scale factors that are positive, zero and negative. For example, what would the image of a shape look like if it is enlarged by a scale factor of -3 rather than +3 ??

 

 

 

 

 

 

 

 

 

 

 

 

 

In the above diagram, the trapezium ABCD is enlarged by a scale factor of 2 to give the same shape A’B’C’D’. So, the enlargement of A is A’; enlargement of AB is A’B’, etc. We can show this transformation as: ABCD–>A’B’C’D’. A’B’C’D’ is the image of ABCD under the enlargement of 2x from the centre point. The order of each point (vertex or corner) is important.

Note: we can find the centre of enlargement by joining and extending the line A’A, B’B, etc. In this case, the centre (or center for our American students) is the origin (0,0).

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10 x 9 x 8 + (7 + 6) x 5 x 4 x (3 + 2) x 1 = 2020

NCEA Level 2 Algebra Problem. Using the information given, the shaded area = 9, that is:
y(y-8) = 9 –> y.y – 8y – 9 =0
–> (y-9)(y+1) = 0, therefore y = 9 (can’t have a distance of – 1 for the other solution for y)
Using the top and bottom of the rectangle,
x = (y-8)(y+2) = (9-8)(9+2) = 11
but, the left side = (x-4) = 11-4 = 7, but rhs = y+? = 9+?, which is greater than the value of the opp. side??
[I think that the left had side was a mistake and should have read (x+4)?]

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