Dilations

Dilation A dilation is a transformation that changes the size of a figure. It can become larger (enlargement) or smaller (reduction), but the shape of the figure does not change. The figures will be similar (same shape but different size).

Scale Factor In two similar geometric figures, the ratio of their corresponding sides is called the scale factor. It tells you if your figure was enlarged or reduced and by how much. (More on this tomorrow) If the scale factor is between 0 and 1, the figure is reduced. If the scale factor is greater than 1, the figure is enlarged. If the scale factor is 1, the figures are congruent (nothing changes) SCALE FACTOR IS NEVER NEGATIVE!

Enlargement or Reduction? Determine if the scale factor demonstrates an enlargement or reduction. Be ready to explain why when I call on you. ¼ 2 1.3 500% (change to decimal first) 5) 45% (change to decimal first) 6) 5 4 7) 2 3

How to Dilate a 2-d Figure Multiply each coordinate by the scale factor. If the scale factor is a percentage, change to a decimal by dropping the % sign and moving the decimal two places to the left. When you see dilation, think MULTIPLY!!! 

Example 1 Dilate triangle A(1,2) B(3, -4) C(-2, 3) by a scale factor of 2 and write the new coordinates. Is the figure being enlarged or reduced?

Example 2 Dilate X(-6,-3) and Y(-5, 3) by a scale factor of 2 3 and write the new coordinates. Is the figure being enlarged or reduced?

Example 3 Dilate C(-3,-9) and D(15, -2) by a scale factor of 400% and write the new coordinates. Is the figure being enlarged or reduced?

You Try Dilate triangle L(0, 14) M(8,-4) N(-12, -2) by a scale factor of 3. A line segment has end points J(4,-8) and K(-10,6). Dilate this figure by a scale factor of ½ and write the new coordinates. Will the new figure be enlarged or reduced? A line segment has end points A(7,-12) and K(-5,10). Dilate this figure by a scale factor of 40% and write the new coordinates. Will the new figure be enlarged or reduced?

Independent Practice Page 74 Got It question A Page 75 Got It question B Page 76 Questions 1-2 Page 77 Questions 1-2, 5a and 5b Page 79 Question 10 Advanced Questions: Page 76 #3, Page 77 #3-4, Page 79 #12 and 13c (AC students try these!! Let’s see if you can figure all of these out.) Answer key is on my desk. Check your work as you go so you can make sure you are doing the problems correctly!! Anything you don’t finish in class is homework.

How to Determine the Scale Factor of 2 Dilated Figures May use x OR y coordinate. The variable k is usually used to represent scale factor.

Example 1 The ordered pair (4, 1) is dilated and is now located at point (12, 3). What scale factor was used for the dilation? (Give as a number and a percentage) The coordinates are multiplied by 3, so k = 3 or the coordinates are dilated by 300%

You Try The coordinates (-16, -6) are dilated and end up at (-8, -3). What scale factor was used for the dilation? (Give as a number and a percentage) The coordinates are reduced by 1/2, so k = 1/2 or the coordinates are dilated by 50%

Example 2 Write the transformation rule for the dilation in the figure.

You Try Write the transformation rule for the dilation in the figure.