4.1 Enlargements and Reductions Math 9

4.1 Enlargements and Reductions Using grid paper, draw an enlargement to the right of the object with dimensions that are twice as large as the original, then draw a reduction below the object with dimensions that are half as large as the original. Measure and label the lengths of the sides in the original, enlargement and reduction.

What is the ratio of the lengths of the sides of the enlargement to the length of the sides of the original? 3.4 cm: 1.7 cm  2:1 Measure some other lengths in the original (tip to opposite tip, indentation to opposite indentation) and the corresponding lengths in the reduction. Is the ratio the same as in the previous step? NO 0.85: 1.7  1:2

Repeat these steps for the reduction. Will any lengths that you measure for either the reduction or the enlargement still be in the same proportion when compared to the original? Lengths for the reduction compared to the original will be 1:2. Lengths for the enlargement compared to the original will be 2:1

The factor by which all dimensions are enlarged or reduced is called the scale factor. In the enlargement above, the scale factor would be 2 while for the reduction the scale factor would be ½. An enlargement occurs when the scale factor is greater than one. A reduction occurs when the scale factor is less than one. The scale factor is the ratio of 𝒂𝒍𝒕𝒆𝒓𝒆𝒅 𝒅𝒊𝒂𝒈𝒓𝒂𝒎 𝒐𝒓𝒊𝒈𝒊𝒏𝒂𝒍 𝒅𝒊𝒂𝒈𝒓𝒂𝒎 .

Enlarge the object below using a scale factor of 3 2 . That means we have to multiply every length by 3 2

Warm-up Partner Practice p.136 # 4, 6, 7, 9, 12, 13