All scale drawings must have a scale written on them. Scales are usually expressed as ratios. Normally for maps and buildings the ratio: Drawing length: Actual length For maps the ratio is normally in the ratio: Map distance: Actual Distance Example: 1cm : 100cm The ratio 1cm:100cm means that for every 1cm on the scale drawing the length will be 100cm in real life Example: 1:10000 The ratio 1:10000 means that the real distance is times the length of one unit on the map or drawing.

 When a figure is dilated, its size is changed by multiplying the length of each side by a scale factor. All angles remain the same and so the new shape (or image) is similar to the original.  Can be found by dividing a new side length by the original side length. When going from a small shape to a larger shape the scale factor is greater than 1. (Enlargement) When going from a small shape to a larger shape the scale factor is greater than 1. (Enlargement) When going from a large shape to a smaller shape the scale factor is When going from a large shape to a smaller shape the scale factor is less than 1. (Reduction) less than 1. (Reduction) 1. Determine the corresponding side lengths. 2. Determine if you are making a larger shape or a smaller shape. 3. Determine if the scale factor is greater than or less than Write the correct ratio.

Scale factor = new measurement old measurement -Scale factor more than 1 => shape gets bigger (Enlargement) - Scale factor less than 1 => shape gets smaller (Reduction) - Congruent shapes are similar shapes with SF = 1 Old measurement x SF = new measurement SF new old

scale model scale factor scale scale drawing

 The scale can be written as a scale factor, which is the ratio of the length or size of the drawing or model to the length of the corresponding side or part on the actual object.  Scale Factor needs to be the SAME UNITS!

This HO gauge model train is a scale model of a historic train. A scale model is a proportional model of a three-dimensional object. Its dimensions are related to the dimensions of the actual object by a ratio called the scale factor. The scale factor of an HO gauge model train is This means that each dimension of the model is of the corresponding dimension of the actual train. 1 87

A scale is the ratio between two sets of measurements. Scales can use the same units or different units. The photograph shows a scale drawing of the model train. A scale drawing is a proportional drawing of an object. Both scale drawings and scale models can be smaller or larger than the objects they represent.

If you have ever seen Jurassic Park, you saw how big the dinosaurs were compared to the people. Pretend that they made a large Human to watch over the animals. What would be the scale factor if a 64 inch person was made to be 160 feet?

The scale factor tells you how many times bigger than “normal” that person really is. You must make all units of measure the same…. 64 inches 160 feet 64 inches 160 x inches 1920 inches = =

Now take the: 64 inches 1920 inches And simplify 1/30 inches This means that the person was created 30 times his normal size.

Identify the scale factor. Additional Example 1: Finding a Scale Factor Scale Drawings and Scale Models RoomBlueprint Length (in.)14418 Width (in.) blueprint length room length = The scale factor is. Write a ratio using one of the dimensions. Simplify =

Try This: Example 1 Insert Lesson Title Here Scale Drawings and Scale Models Identify the scale factor. Model AircraftBlueprint Length (in.)122 Wing span (in.)183 blueprint length aircraft length = 2 12 = 1616 The scale factor is Write a ratio using one of the dimensions. Simplify.

A photograph was enlarged and made into a poster. The poster is 20.5 inches by 36 inches. The scale factor is. Find the size of the photograph. Additional Example 2: Using Scale Factors to Find Unknown Lengths 5151 Think: poster photo = l = l = 36 l = 7.2 Write a proportion to find the length l. Find the cross products. Divide.

A photograph was enlarged and made into a poster. The poster is 20.5 inches by 36 inches. The scale factor is. Find the size of the photograph. Scale Drawings and Scale Models 5151 Think: poster photo = w = w = 20.5 w = 4.1 Write a proportion to find the width w. Find the cross products. Divide. The photo is 7.2 in. long and 4.1 in. wide. Additional Example 2 Continued

Try This: Example 2 Scale Drawings and Scale Models Mary’s father made her a dollhouse which was modeled after the blueprint of their home. The blueprint is 24 inches by 45 inches. The scale factor is. Find the size of the dollhouse Think: dollhouse blueprint = l = 45 · 1.5 l = 67.5 Write a proportion to find the length l. Find the cross products. Multiply. l 45 = 1.5 1

Try This 2 Continued Scale Drawings and Scale Models w 24 = w = 24 · 1.5 w = 36 Write a proportion to find the width w. Find the cross products. Multiply. The dollhouse is 67.5 inches long and 36 inches wide. Think: dollhouse blueprint = Mary’s father made her a dollhouse which was modeled after the blueprint of their home. The blueprint is 24 inches by 45 inches. The scale factor is. Find the size of the dollhouse

Lesson Quiz: Part 1 Insert Lesson Title HereScale Drawings and Scale Models Identify the scale factor. Statue of LibertyModel Height (in.) 1, inches, or 12 feet On a scale drawing, a kitchen wall is 6 inches long. The scale factor is. What is the length of the actual wall? 1 24

Keep like units in the same fraction. Inches = yards Inches yards

 There is more than one way to set up a proportion correctly!  Cross Multiply!  Use common sense!

 Tom is drawing a blueprint for a rectangular shed he wants to build. The scale factor is 1 ft. to ¼ inch. If the dimensions of the blueprint are 1 ¼ in. by 2 inches, what are the actual dimensions of the shed going to be?

¾ inch to 1 foot  If the length in inches is 2 ¼ inch, what would the actual length be in feet ?

Scale Drawings On Maps Footprints of houses Vehicle design

Scale 1 cm = 1 m 6cm Length of units = 6 m 5

Scale 2 cm = 1 m pool path decking 7

When objects are too small or too large to be drawn or constructed at actual size, people use a scale drawing or a model. The scale drawing of this tree is 1:500 If the height of the tree on paper is 20 inches, what is the height of the tree in real life?

The scale is the relationship between the measurements of the drawing or model to the measurements of the object. In real-life, the length of this van may measure 240 inches. However, the length of a copy or print paper that you could use to draw this van is a little bit less than 12 inches

 Map Scales (Legends) are used to find distances on a map.  For example, if your map legend tells you that ½ of an inch represents 50 miles, how could you find the mileage for a 2 inch distance on the map?

Ratios and proportions can be used to find distances using a scale. Example: 1 inch = 15 miles The distance from Jacksonville to Smithtown on a map is 4 inches. How many miles are between these cities? 1 in. 15 mi. = 4 in n 1n =60 n = 60 The distance between the two cities is 60 miles.