SCALE FACTORS AND SIMILARITY Introducing scale factor.

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Presentation transcript:

SCALE FACTORS AND SIMILARITY Introducing scale factor

Enlargements and Reductions  When you want to either enlarge or reduce the size of an object, you must do so by a constant factor.  In other words, you must either decrease all dimensions by the same amount, or increase all dimensions by the same amount.  If you don’t use a constant factor, the object will not be represented accurately.  

Scale factor  When we refer to a scale factor, we are talking about the constant factor by which all dimensions of an object are enlarged or reduced in a scale drawing.  Example of an enlargement:  Draw a rectangle that has a width of 1 cm and a length of 3 cm.  Now draw the rectangle twice as large. Hmmm – how do you calculate that???  Simple: multiply each measurement by a scale factor of 2. (1 x 2 = 2and 3 x 2 = 6)  Now you have a rectangle that is 2 cm wide and 6 cm long.

Scale factor  Remember: when we refer to a scale factor, we are talking about the constant factor by which all dimensions of an object are enlarged or reduced in a scale drawing.  Example of a reduction:  Draw another rectangle that has a width of 1 cm and a length of 3 cm.  Now draw the rectangle half as large. Hmmm – how do you calculate that???  Simple: multiply each measurement by a scale factor of.5. (1 x.5 =.5and 3 x.5 = 1.5)  Now you have a rectangle that is.5 cm wide and 1.5 cm long.

Scale factor  Scale factor indicates whether an object is either enlarged or reduced.  A scale factor that is greater than 1 means that the object is being enlarged.  A scale factor that is less than 1 indicates that the object is being reduced.  A scale factor that is equal to 1 indicates that there is no change in the size of the object.

Using graph paper to enlarge and reduce  Jewellery designers often use graph paper to enlarge designs while they are creating them.  Interior designers often use graph paper to proportionately represent the layouts of rooms. Naturally, you could not make a blueprint the actual size of the room, so they use graph paper and use a reduced scale factor to show the layout.

Practice makes perfect  Homework:  Page 136 and 137 #4a, 5, 6b, 7, 8, 9, 12, 17a,b