Case Study Based- 2

SCALE FACTOR AND SIMILARITY

SCALE FACTOR

A scale drawing of an object is the same shape as the object but a different size.

The scale of a drawing is a comparison of the length used on a drawing to the length it represents. The scale is written as a ratio.

SIMILAR FIGURES

The ratio of two corresponding sides in similar figures is called the scale factor.

Scale factor = length in image / corresponding length in object

If one shape can become another using Resizing then the shapes are Similar.

Rotation or Turn

Reflection or Flip

Translation or Slide

Hence, two shapes are Similar when one can become the other after a resize, flip, slide or turn.

(a) A model of a boat is made on the scale of 1:4. The model is 120cm long. The full size of the boat has a width of 60cm. What is the width of the scale model?

(i) 20 cm (ii) 25 cm (iii) 15 cm (iv)240 cm

(b) What will affect the similarity of any two polygons?

(i) They are flipped horizontally

(ii)They are dilated by a scale factor

(iii)They are translated down

(iv)They are not the mirror image of one another

(c) If two similar triangles have a scale factor of a: b. Which statement regarding the two triangles is true?

(i)The ratio of their perimeters is 3a : b

(ii)Their altitudes have a ratio a:b

(iii)Their medians have a ratio